AMC 10 Weekly Practice Round 2

Complete problem set with solutions and individual problem pages

Problem 6 Medium

The total number of students in School A and School B is in the ratio of 4:5.

The number of boys in School A and School B is in the ratio of 2:3.

If School A has 230 girls and School B has 250 girls, how many students are there in total across both schools?

  • A.

    845

  • B.

    855

  • C.

    865

  • D.

    875

  • E.

    885

Answer:B

Let the number of boys in School A be 2x, then the number of boys in School B is 3x.

According to the given ratio, we can set up the proportion:

(2x + 230) : (3x + 250) = 4 : 5

Using the property of proportions (cross multiplication), we get:

5(2x + 230) = 4(3x + 250)

Solving the equation gives:

x = 75

Therefore, School A has 2 \times 75 = 150 boys,

and School B has 3 \times 75 = 225 boys.

The total number of students in both schools is: 150 + 225 + 230 + 250 = 855.

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