The sum of three numbers is 98. The first number is 2/3 of the second, and the second is 5/8 of the third. What is the second number?

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- Sep 9th 2008, 10:43 AMamywright00The sum of three numbers
The sum of three numbers is 98. The first number is 2/3 of the second, and the second is 5/8 of the third. What is the second number?

- Sep 9th 2008, 11:02 AMSoroban
Hello, Amy!

Quote:

The sum of three numbers is 98.

The first number is 2/3 of the second, and the second is 5/8 of the third.

What is the second number?

Let the three numbers be: $\displaystyle a,b,c.$

"Their sum is 98": .$\displaystyle a + b + c \:=\:98$ .[1]

"The first is 2/3 of the second": .$\displaystyle a \:=\:\frac{2}{3}b$ .[2]

"The second is 5/8 of the third": .$\displaystyle b \:=\:\frac{5}{8}c \quad\Rightarrow\quad c \:=\:\frac{8}{5}b$ .[3]

Substitute [2] and [3] into [1]: .$\displaystyle \frac{2}{3}b + b + \frac{8}{5}b \:=\:98$

Multiply by 15: .$\displaystyle 10b + 15b + 24b \:=\:1470 \quad\Rightarrow\quad 49b \:=\:1470$

. . Therefore: .$\displaystyle \boxed{b \;=\;30}$

- Sep 9th 2008, 01:34 PMamywright00
I do not understand how they all became b