The sum of two numbers is twenty. Three times the smaller number is equal to two times the larger number. Find the smaller number.
A) 3
B) 11
C) 8
D) 7
E) 17

Question

Quizplus · Accepted Answer

Let's call the smaller number "x" and the larger number "y". 
From the first sentence, we know that: 
x + y = 20 
From the second sentence, we know that: 
3x = 2y 
We can use substitution to solve for one of the variables. 
Rearranging the second equation: 
y = (3/2)x 
Now we can substitute this value for y in the first equation: 
x + (3/2)x = 20 
Combining like terms: 
(5/2)x = 20 
Multiplying both sides by (2/5): 
x = 8 
Therefore, the smaller number is 8.

The Sum of Two Numbers Is Twenty