If red to blue is 5:2 and there are 35 red objects, how many blue objects are there?

If red to blue is 5:2 and there are 35 red objects, how many blue objects are there?

• A. 10
• B. 12
• C. 14
• D. 18

Answer: (C)

The problem hinges on scaling a given ratio. Red to blue is 5:2, meaning for every 5 red objects there are 2 blue objects. If there are 35 red objects, that’s 35 ÷ 5 = 7 groups of 5 red. Each group has 2 blue, so 7 × 2 = 14 blue objects. Check: 14 blue with 35 red keeps the 5:2 ratio since 35 is (5/2)×14. Other blue counts don’t fit the ratio with 35 red (for example, 10 blue would pair with 25 red, 12 blue with 30 red, 18 blue with 45 red). So there are 14 blue objects.

The problem hinges on scaling a given ratio. Red to blue is 5:2, meaning for every 5 red objects there are 2 blue objects. If there are 35 red objects, that’s 35 ÷ 5 = 7 groups of 5 red. Each group has 2 blue, so 7 × 2 = 14 blue objects. Check: 14 blue with 35 red keeps the 5:2 ratio since 35 is (5/2)×14. Other blue counts don’t fit the ratio with 35 red (for example, 10 blue would pair with 25 red, 12 blue with 30 red, 18 blue with 45 red). So there are 14 blue objects.