James has $10 in 5 cent and 10 cent coins in his change jar and counts 157 in total. How many 10 cent coins does he have

Question

I need this question solves step by step 

Answer 1

This may not be the most efficient way, but it works:

I used x for the number of 5 cent coins and y for the number of 10 cent coins.

 

(A) The number of coins you want to find: x + y = 157

(B) The sum of money you want to have: $10 = 0.05x + 0.1y

 

Isolate a variable from equation (A) (I chose y):

y = 157 - x

 

Substitute that for y in the sum-of-money equation (B):

$10 = 0.05x + 0.1(157 - x)

 

Factor the equation:

$10 = 0.05x + 15.7 - 0.1x

 

Simplify:

$10 = -0.05x + 15.7

 

Solve for x:

($10 - 15.7)/(-.05) = x

 

x = 114

There are 114 5-cent pieces.

 

Since the question was the number of 10 cent pieces, plug x back into the number-of-coins equation (A):

114 + y = 157

 

Solve for y.

y = 157 - 114

 

Therefore . . .

y = 43

and there are 43 10-cent pieces.