ACT Math Ratios Proportions and Percentages Quiz

To find the number of girls, first determine the total parts in the ratio 3:5, which is 8. Since there are 24 boys (3 parts), each part equals 8 (24 boys ÷ 3 parts). Therefore, the number of girls (5 parts) is 8 × 5 = 40.

To maintain the ratio of flour to sugar (2:3), first determine how many sets of 3 cups of sugar are in 9 cups. There are 3 sets (9 ÷ 3 = 3). Since each set requires 2 cups of flour, multiply 2 cups by 3 sets to find that you need 6 cups of flour (2 × 3 = 6).

To find 25% of 80, you can multiply 80 by 0.25 (which represents 25%). This calculation gives you 80 × 0.25 = 20. Thus, 25% of 80 is 20.

To find the final price after a 20% discount on a $50 item, first calculate the discount amount: 20% of $50 is $10. Subtract the discount from the original price: $50 - $10 = $40. Thus, the final price after the discount is $40.

To find the actual distance between the two cities, multiply the distance on the map (3 inches) by the scale factor (5 miles per inch). Thus, 3 inches x 5 miles/inch equals 15 miles. Therefore, the cities are 15 miles apart.

To find what percent 50 is of 200, divide 50 by 200 and then multiply by 100. This calculation (50 ÷ 200 × 100) results in 25%. Thus, 50 represents 25% of 200.

To solve the proportion x:6 = 4:8, we can cross-multiply. This gives us 8x = 24. Dividing both sides by 8, we find x = 3. Thus, the value of x that maintains the equality of the ratios is 3.

To find the percentage score, divide the student's score by the total possible score and multiply by 100. In this case, \( \frac{85}{100} \times 100 = 85\% \). This means the student achieved 85 out of a possible 100 points, resulting in an 85% score.

To calculate the percent increase, subtract the original price from the new price, which gives $10. Then, divide this increase by the original price of $40, resulting in 0.25. Finally, multiply by 100 to convert it to a percentage, yielding a 25% increase.

To find the number of apples, use the ratio of apples to oranges, which is 7:3. If there are 30 oranges, set up a proportion: (7/3) = (x/30). Solving for x gives x = 70 apples. Thus, there are 70 apples corresponding to 30 oranges.

To find 15% of 120, multiply 120 by 0.15 (which is the decimal form of 15%). This calculation results in 18, as 120 multiplied by 0.15 equals 18. Thus, 15% of 120 is 18.

To find the number, set up the equation where 40% of the number equals 32. This can be expressed as 0.4x = 32. Solving for x, divide both sides by 0.4, yielding x = 32 / 0.4, which simplifies to x = 80. Thus, the number is 80.