The numbers x, y, z are proportional to 2, 3, 5. The sum of x, y, and z is 100. The number y is given by the equation y=ax-10. Then a is:

1957 AMC 12 Problem 8

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The numbers

x,

y,

z

are proportional to

2,

3,

5.

The sum of

x,

y,

and

z

100.

The number

y

is given by the equation

y=ax-10.

Then

a

is:

2

\dfrac23

3

\dfrac52

4

Write

x,y,z

2t,3t,5t

Their sum determines

t

, after which substitute

x

and

y

into the given equation

Let

x=2t,

y=3t,

and

z=5t.

Since

10t=100,

we get

t=10,

x=20

and

y=30.

Thus

30=20a-10,

and

a=2.

Therefore, the correct answer is A.