# The sum of three numbers

• Sep 9th 2008, 10:43 AM
amywright00
The 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 AM
Soroban
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 PM
amywright00
I do not understand how they all became b