{"questions":[{"uuid":"7a56623a-2c34-41a8-b4d6-fa3496ab47ee","question":"A blueprint of a room is drawn at a scale of 1:50. If the actual length of the room is 100 meters, what is the length on the blueprint?","answer":"

2

meters","alternatives":["

5

meters","

50

meters","

10

meters"],"answerExplanation":"In a 1:50 scale drawing, 1 unit on the blueprint represents 50 units in real life. So, for an actual length of 100 meters, the length on the blueprint would be

100 / 50 = 2

meters.","hint":"Divide the actual length by the scale factor:

100 / 50

.","imageEnabled":false,"duration":30,"latexEnabled":false,"audioEnabled":false,"htmlEnabled":true,"questionId":"7a56623a-2c34-41a8-b4d6-fa3496ab47ee"},{"uuid":"3beb57dc-e891-44ad-abe7-8a0043753691","question":"Sarah earns a simple interest of $60 on a principal amount of $200 over 3 years. What is the annual interest rate?","answer":"10%","alternatives":["15%","5%","8%"],"answerExplanation":"The formula for simple interest is

I = P \\times R \\times T

. Here,

I

is $60,

P

is $200, and

T

is 3 years. Rearranging the formula to find the rate:

R = \\frac{I}{P \\times T}

. So,

R = \\frac{60}{200 \\times 3} = 0.1

, which is 10%.","hint":"Use the simple interest formula:

I = P \\times R \\times T

. Solve for

R

.","imageEnabled":false,"duration":30,"latexEnabled":false,"audioEnabled":false,"htmlEnabled":true,"questionId":"3beb57dc-e891-44ad-abe7-8a0043753691"},{"uuid":"79d43bf0-0314-4b9b-b63f-2222af4a2f9a","question":"John has a scale drawing of a garden where 1 centimeter represents 4 meters. If the garden's width on the drawing is 3 centimeters, what is the actual width of the garden?","answer":"12 meters","alternatives":["9 meters","3 meters","7 meters"],"answerExplanation":"In the scale drawing, each centimeter represents 4 meters. So, if the width on the drawing is 3 centimeters, the actual width is

3 \\times 4 = 12

meters.","hint":"Multiply the drawing measurement by the scale factor:

3 \\times 4

.","imageEnabled":false,"duration":30,"latexEnabled":false,"audioEnabled":false,"htmlEnabled":true,"questionId":"79d43bf0-0314-4b9b-b63f-2222af4a2f9a"},{"uuid":"b4ff9f05-ac88-47ee-9fb4-847b363b8f99","question":"Emma deposits $400 in a savings account with a simple interest rate of 5% per year. How much interest will she earn after 2 years?","answer":"$40","alternatives":["$60","$20","$80"],"answerExplanation":"Using the simple interest formula

I = P \\times R \\times T

, where

P

is $400,

R

is 0.05 (5%), and

T

is 2 years, we calculate:

I = 400 \\times 0.05 \\times 2 = 40

. So, Emma earns $40 in interest.","hint":"Use the formula

I = P \\times R \\times T

to calculate the interest.","imageEnabled":false,"duration":30,"latexEnabled":false,"audioEnabled":false,"htmlEnabled":true,"questionId":"b4ff9f05-ac88-47ee-9fb4-847b363b8f99"},{"uuid":"e199be09-269d-465a-afea-109685e80281","question":"Liam borrows $500 at a simple interest rate of 6% per year. How much total interest will he pay after 4 years?","answer":"$120","alternatives":["$60","$180","$240"],"answerExplanation":"Using the simple interest formula

I = P \\times R \\times T

, where

P

is $500,

R

is 0.06 (6%), and

T

is 4 years, we find:

I = 500 \\times 0.06 \\times 4 = 120

. So, Liam pays $120 in interest.","hint":"Plug the values into the formula

I = P \\times R \\times T

.","imageEnabled":false,"duration":30,"latexEnabled":false,"audioEnabled":false,"htmlEnabled":true,"questionId":"e199be09-269d-465a-afea-109685e80281"},{"uuid":"c1a9aa6a-bbbe-4bdb-a7be-68a29029adc2","question":"A painting is created at a scale of 1:10. If the height of the painting is 8 cm in the scale drawing, what is the actual height in centimeters?","answer":"80 cm","alternatives":["18 cm","800 cm","40 cm"],"answerExplanation":"In a 1:10 scale, each centimeter in the drawing represents 10 real centimeters. Therefore, the actual height is

8 \\times 10 = 80

cm.","hint":"Multiply the scale drawing height by the scale factor to find the actual height.","imageEnabled":false,"duration":30,"latexEnabled":false,"audioEnabled":false,"htmlEnabled":true,"questionId":"c1a9aa6a-bbbe-4bdb-a7be-68a29029adc2"},{"uuid":"4cddfa01-45c6-4554-afbb-73c5231ac761","question":"If you invest $1000 at a simple interest rate of 5% per year, how much interest will you earn after 3 years?","answer":"$150","alternatives":["$100","$200","$250"],"answerExplanation":"Simple interest is calculated using the formula Interest = Principal x Rate x Time. Here, it's $1000 x 0.05 x 3 = $150.","hint":"Use the formula for simple interest: Interest = Principal x Rate x Time.","imageEnabled":false,"duration":30,"latexEnabled":false,"audioEnabled":false,"htmlEnabled":true,"questionId":"4cddfa01-45c6-4554-afbb-73c5231ac761"},{"uuid":"dbaae35c-3360-4178-ada8-253ca3d4b5a7","question":"You deposit $600 in a savings account with a simple interest rate of 3% per year. How much total money will you have in the account after 5 years?","answer":"$690","alternatives":["$750","$720","$630"],"answerExplanation":"The interest earned is calculated as Principal x Rate x Time, which is $600 x 0.03 x 5 = $90. The total amount in the account after 5 years is the initial deposit plus the interest: $600 + $90 = $690.","hint":"Calculate the interest and add it to your initial deposit to find the total amount.","imageEnabled":false,"duration":30,"latexEnabled":false,"audioEnabled":false,"htmlEnabled":true,"questionId":"dbaae35c-3360-4178-ada8-253ca3d4b5a7"},{"uuid":"d7a5a1dd-a8e2-440b-86da-4d08255900f6","question":"If you borrow $500 from a bank with a simple interest rate of 4% per year, how much interest will you owe after 2 years?","answer":"$40","alternatives":["$20","$30","$50"],"answerExplanation":"The interest owed can be calculated using the formula Interest = Principal x Rate x Time. Here, it is $500 x 0.04 x 2 = $40.","hint":"Use the formula for simple interest to find out how much you will owe after 2 years.","imageEnabled":false,"duration":30,"latexEnabled":false,"audioEnabled":false,"htmlEnabled":true,"questionId":"d7a5a1dd-a8e2-440b-86da-4d08255900f6"},{"uuid":"3135977a-1f8b-4ae3-9165-26b72ce7dfcb","question":"A scale drawing shows a rectangular room with dimensions 4 cm by 3 cm. If the actual width of the room is 6 meters, what is the actual length of the room?","answer":"8 meters","alternatives":["10 meters","9 meters","12 meters"],"answerExplanation":"The scale factor can be found by comparing the drawing's width to the actual width: 3 cm represents 6 meters, so each cm represents 2 meters. Therefore, the actual length of the room is 4 cm * 2 meters/cm = 8 meters.","hint":"Use the scale provided by the width to find the length.","imageEnabled":false,"duration":30,"latexEnabled":false,"audioEnabled":false,"htmlEnabled":true,"questionId":"3135977a-1f8b-4ae3-9165-26b72ce7dfcb"}]}

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