Question

John is taking a Math test with 75 problems. The problems were of three types:

10 problems were number related,
30 were algebra and
35 were geometry.

John answered 70% of the number problems correctly, 40% of the algebra correctly and 60% of the geometry correctly.

He had to answer 60% of all the problems correctly to pass but didn’t get it. How many more problems had John to answer to pass??

Please explain how to calculate this. (Without an calculator)

Answer 1

For each category of problem type, John correctly answered...

• Number problems: 70% of 10 = 7

• Algebra problems: 40% of 30 = 12

• Geometry problems: 60% of 35 = 21

Total correctly answered: 7 + 12 + 21 = 40

Total problems available: 10 + 30 + 35 = 75

John got 40/75 correct. He needed to get at least 60%, and 60% of 75 = 45, so he had to answer 5 more correctly in order to pass.

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In case you're not sure how to get the number of correctly answered problems: if you want to find, for example, 23% of 315, you can break up the percentage as

`23\%=2\cdot10\%+3\cdot1\%`

Finding 10% and 1% of any number is easy, just move the decimal point accordingly:

• 10% of 315 = 31.5
• 1% of 315 = 3.15

Then 23% of 315 = 2(31.5) + 3(3.15) = 72.45.