7:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Quiz 6\",\"description\":\"Ratios and rates quiz\",\"url\":\"https://theschoolofmathematics.com/quiz/psat-8-9-ratios-rates-proportional-relationships-quiz-6\",\"educationalLevel\":\"Advanced\",\"numberOfQuestions\":10,\"isAccessibleForFree\":true,\"about\":{\"@type\":\"Thing\",\"name\":\"Problem-Solving and Data Analysis: Ratios, Rates, Proportional Relationships\"}}"}}],["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https://theschoolofmathematics.com\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Quizzes\",\"item\":\"https://theschoolofmathematics.com/quiz\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Quiz 6\",\"item\":\"https://theschoolofmathematics.com/quiz/psat-8-9-ratios-rates-proportional-relationships-quiz-6\"}]}"}}],["$","div",null,{"className":"bg-gradient-to-b from-white via-gray-50 to-white","children":["$","div",null,{"className":"container mx-auto px-4 py-8 md:py-12","children":[["$","div",null,{"className":"mb-12","children":["$undefined",["$","div",null,{"className":"mb-8","children":["$","h1",null,{"className":"text-4xl md:text-5xl lg:text-6xl font-bold text-gray-900 mb-4","children":"Quiz 6"}]}],["$","div",null,{"className":"bg-white rounded-2xl shadow-lg p-6 md:p-8 border border-gray-200","children":[["$","div",null,{"className":"text-lg md:text-xl text-gray-700 mb-8 leading-relaxed prose prose-lg max-w-none","dangerouslySetInnerHTML":{"__html":"

Ratios and rates quiz

"}}],["$","div",null,{"className":"grid grid-cols-2 md:grid-cols-3 gap-4","children":["$undefined",["$","div",null,{"className":"flex items-center gap-3 p-4 bg-gray-50 rounded-xl border border-gray-200","children":[["$","div",null,{"className":"w-10 h-10 bg-gray-900 rounded-lg flex items-center justify-center flex-shrink-0","children":["$","svg",null,{"className":"w-5 h-5 text-white","fill":"none","stroke":"currentColor","viewBox":"0 0 24 24","children":["$","path",null,{"strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"d":"M8.228 9c.549-1.165 2.03-2 3.772-2 2.21 0 4 1.343 4 3 0 1.4-1.278 2.575-3.006 2.907-.542.104-.994.54-.994 1.093m0 3h.01M21 12a9 9 0 11-18 0 9 9 0 0118 0z"}]}]}],["$","div",null,{"children":[["$","div",null,{"className":"text-xs text-gray-500 font-medium","children":"Questions"}],["$","div",null,{"className":"text-sm font-bold text-gray-900","children":10}]]}]]}],["$","div",null,{"className":"flex items-center gap-3 p-4 bg-gray-50 rounded-xl border border-gray-200","children":[["$","div",null,{"className":"w-10 h-10 bg-gray-900 rounded-lg flex items-center justify-center flex-shrink-0","children":["$","svg",null,{"className":"w-5 h-5 text-white","fill":"none","stroke":"currentColor","viewBox":"0 0 24 24","children":["$","path",null,{"strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"d":"M9 12l2 2 4-4m6 2a9 9 0 11-18 0 9 9 0 0118 0z"}]}]}],["$","div",null,{"children":[["$","div",null,{"className":"text-xs text-gray-500 font-medium","children":"Level"}],["$","div",null,{"className":"text-sm font-bold text-gray-900","children":"Advanced"}]]}]]}],["$","div",null,{"className":"flex items-center gap-3 p-4 bg-gray-50 rounded-xl border border-gray-200","children":[["$","div",null,{"className":"w-10 h-10 bg-gray-900 rounded-lg flex items-center justify-center flex-shrink-0","children":["$","svg",null,{"className":"w-5 h-5 text-white","fill":"none","stroke":"currentColor","viewBox":"0 0 24 24","children":["$","path",null,{"strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"d":"M7 7h.01M7 3h5c.512 0 1.024.195 1.414.586l7 7a2 2 0 010 2.828l-7 7a2 2 0 01-2.828 0l-7-7A1.994 1.994 0 013 12V7a4 4 0 014-4z"}]}]}],["$","div",null,{"children":[["$","div",null,{"className":"text-xs text-gray-500 font-medium","children":"Category"}],["$","div",null,{"className":"text-sm font-bold text-gray-900","children":"Problem-Solving and Data Analysis: Ratios, Rates, Proportional Relationships"}]]}]]}]]}]]}]]}],["$","$L17",null,{"quiz":{"id":2442,"prismaId":"cmpz9rkwc0esfjgllbna2fbn0","slug":"psat-8-9-ratios-rates-proportional-relationships-quiz-6","title":{"rendered":"Quiz 6"},"content":{"rendered":"

Practice on ratios, rates, and proportional relationships.

"},"excerpt":{"rendered":"

Ratios and rates quiz

"},"featured_media":0,"featured_media_url":"$undefined","acf":{"duree_estimee":"$undefined","niveau_difficulte":"Advanced","categorie":"Problem-Solving and Data Analysis: Ratios, Rates, Proportional Relationships","nombre_questions":10,"score_minimum":70,"ordre_questions":"Fixe","questions":[{"id":"cmrk8ezlz0xkcjg8wwq8cns90","texte_question":"

A spacecraft travels at a constant speed of $$3.25$$ miles per second. What is its speed in yards per hour? $$(1\\text{ mile}=1760\\text{ yards})$$

","type_question":"QCM","explication":"

Convert miles per second to yards per second.

$$3.25\\times1760=5720$$

There are $$3600$$ seconds in $$1$$ hour.

Multiply yards per second by $$3600$$.

$$5720\\times3600=20592000$$

Final answer: $$20592000$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$20592000$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$18720000$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$20592$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$11440000$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ezm20xkijg8wfk31v3y4","texte_question":"

A county has a population density of $$185$$ people per square mile and a total population of $$92500$$. What is the area of the county, in square miles?

","type_question":"TexteLibre","explication":"

Use the population density formula.

$$density=\\frac{population}{area}$$

Solve for area.

$$area=\\frac{population}{density}$$

Substitute the values.

$$area=\\frac{92500}{185}$$

Divide.

$$area=500$$

Final answer: $$500$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

500

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ezm40xkljg8wmbr6l86c","texte_question":"

A city has a total area of $$75$$ square miles, of which $$12$$ square miles are water. If the population is $$315000$$, which value is closest to the population density per square mile of land?

","type_question":"QCM","explication":"

Find the land area.

$$75-12=63$$

Use the density formula.

$$density=\\frac{population}{land\\ area}$$

Substitute the values.

$$density=\\frac{315000}{63}$$

Divide.

$$density=5000$$

Final answer: $$5000$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$4200$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$4500$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$5000$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$6000$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ezm60xkrjg8wywyhuxeh","texte_question":"

Objects A and B move at constant speeds. Object A travels twice as fast as object B. If object A travels $$6x$$ meters in $$y$$ seconds, how many seconds does it take object B to travel $$18x$$ meters?

","type_question":"QCM","explication":"

Find the speed of object A.

$$speed_A=\\frac{6x}{y}$$

Object A travels twice as fast as object B.

So, object B has half the speed of object A.

$$speed_B=\\frac{1}{2}\\cdot\\frac{6x}{y}$$

$$speed_B=\\frac{3x}{y}$$

Find the time for object B to travel $$18x$$ meters.

$$time=\\frac{distance}{speed}$$

$$time=\\frac{18x}{\\frac{3x}{y}}$$

Multiply by the reciprocal.

$$time=18x\\cdot\\frac{y}{3x}$$

Simplify.

$$time=6y$$

Final answer: $$6y$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$3y$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$6y$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$9y$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$12y$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ezm80xkxjg8w7hsmqgxr","texte_question":"

A runner moves at a speed of $$\\frac{5}{12}$$ feet per second. What is this speed in yards per second? $$(3\\text{ feet}=1\\text{ yard})$$

","type_question":"QCM","explication":"

Convert feet to yards.

$$3$$ feet equals $$1$$ yard.

Divide the speed in feet per second by $$3$$.

$$\\frac{5}{12}\\div3$$

Rewrite division as multiplication by the reciprocal.

$$\\frac{5}{12}\\times\\frac{1}{3}$$

Multiply.

$$\\frac{5}{36}$$

Final answer: $$\\frac{5}{36}$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$\\frac{5}{36}$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\frac{5}{4}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{15}{12}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{5}{3}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ezmb0xl3jg8w4b0c97cd","texte_question":"

A worker earns $$18.75$$ dollars per hour. If the worker earns $$18.75x$$ dollars for $$x$$ hours, which expression represents the total earnings for $$4x$$ hours?

","type_question":"QCM","explication":"

The worker earns $$18.75$$ dollars per hour.

For $$4x$$ hours, multiply the hourly rate by $$4x$$.

$$18.75(4x)$$

Final answer: $$18.75(4x)$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$75x$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$4(18.75x)$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$18.75(4x)$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$75+x$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ezmd0xl9jg8w311n98nr","texte_question":"

A cube has edge length $$2.5$$ cm and a mass of $$6.25$$ grams. What is its density, in grams per cubic centimeter?

","type_question":"TexteLibre","explication":"

Find the volume of the cube.

$$2.5^3=15.625$$

Use the density formula.

$$density=\\frac{mass}{volume}$$

Substitute the values.

$$density=\\frac{6.25}{15.625}$$

Divide.

$$density=0.4$$

Final answer: $$0.4$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

0.4

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ezmf0xlcjg8wxbahgc37","texte_question":"

Rectangle A has length $$12$$ and width $$w$$. Rectangle B has length $$18$$ and the same ratio of length to width as rectangle A. What is the width of rectangle B?

","type_question":"QCM","explication":"

Rectangle A has length $$12$$ and width $$w$$.

Rectangle B has length $$18$$.

Find the scale factor from rectangle A to rectangle B.

$$\\frac{18}{12}=\\frac{3}{2}$$

The width must be multiplied by the same scale factor.

$$w\\cdot\\frac{3}{2}=\\frac{3}{2}w$$

Final answer: $$\\frac{3}{2}w$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$\\frac{3}{2}w$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\frac{2}{3}w$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$w+6$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$w-6$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ezmh0xlijg8wrxh43ukp","texte_question":"

A solid cube has density $$900$$ kg/m$$^3$$ and side length $$0.7$$ meters. What is its mass, to the nearest whole number?

","type_question":"QCM","explication":"

Find the volume of the cube.

$$0.7^3=0.343$$

Use the formula:

$$mass=density\\times volume$$

Substitute the values.

$$mass=900\\times0.343$$

Multiply.

$$mass=308.7$$

Round to the nearest whole number.

Final answer: $$309$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$309$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$343$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$441$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$567$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8ezmk0xlojg8wfm2st4mr","texte_question":"

A food item contains $$9$$ grams of protein and costs $$0.45$$ dollars. Another contains $$12$$ grams of protein and costs $$0.60$$ dollars. What is the ratio of the cost per gram of the first item to the second?

","type_question":"QCM","explication":"

Find the cost per gram for the first item.

$$\\frac{0.45}{9}=0.05$$

Find the cost per gram for the second item.

$$\\frac{0.60}{12}=0.05$$

Compare the costs per gram.

$$0.05:0.05=1:1$$

Final answer: $$1:1$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$1:1$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$2:3$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$3:2$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$4:5$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]}]},"categories":["problem-solving-and-data-analysis-ratios-rates-proportional-relationships"],"date":"2026-06-04T09:04:48.012Z","modified":"2026-07-14T05:49:52.963Z"}}],["$","div",null,{"className":"container mx-auto px-4 pb-12","children":["$","$L18",null,{"targetType":"quiz","targetSlug":"psat-8-9-ratios-rates-proportional-relationships-quiz-6"}]}]]}]}]]

Quiz 6

Comments

Leave a comment