2003 AMC 10A Problem 13

Problem 13 of 25IntermediateAlgebra

The sum of three numbers is

20.

The first is

4

times the sum of the other two. The second is seven times the third. What is the product of all three?

Show solution

Solution

Let the numbers be

a,

b,

c.

Since

a = 4(b + c),

we get

4(b + c) + (b + c) = 20,

b + c = 4

and

a = 16.

With

b = 7c,

we have

7c + c = 4,

c = \dfrac{1}{2}

and

b = \dfrac{7}{2}.

The product is

16 \cdot \dfrac{7}{2} \cdot \dfrac{1}{2} = 28.

Thus, the correct answer is A.

Tagged: system of equations · substitution