A number is twice a smaller number. The average of the two numbers is 117. What is the larger number?

Question

9. 5th grade math

 

Answer 1

Marley,

 

Turn what were told into a system of equations.

 

l=2s

(l+s)/2=117

 

Substitute to get a formula with one variable

 

(2s + s)/2=117

 

Combine terms

 

3s/2=117

 

Divide both sides by three

 

s/2=39

 

Multiply both sides by 2

 

s=78

 

Plug the solved variable back into one of the original formulas to solve for the other.

 

l=2(78)

l=156

 

Evaluate answer against originally problem.

 

1. Is the 156 twice 78. Yes it is.

2. Is 117 the average of 156 and 78. Yes it is.

 

The answers 156 is a winner.

 

Answer 2

Hi Marley--

 

think of the smaller number as "s" and the larger one as "2s".

 

They are 2 numbers whose average is 117, which means you divided some other number by 2 to get to 117.

 

If ? divided by 2 = 117, that means that 117 x 2 = ?

 

so your "?" is 234.

 

SO the two numbers ("s" and "2s") add up to 234, or

 

s + 2s = 234, or

 

3s = 234, which means that...

 

s = 78, and

 

2s = 156. And...

 

156 + 78 = 234, and

 

234 divided by 2 = 117.

 

So it checks. :-)

 

Hope this helps!

 

Matt in NY