A coin bank contains 31 coins. There is one quarter and the rest are dimes and nickels. The combined value is $2.35. How many dimes are there?

Question

I need help on this math question i don't understand word problems

Answer 1

Hi Brook, let d represent the dimes, and n represent the nickels. We can set up to equations.

 

Number of coins:

 

d + n + 1 (represents the quarter) = 31

 

Value of the coins:

 

.10d + .05n + .25*1 = 2.35

 

We can eliminate the quarter by subtracting it from both sides of the equations giving:

 

     d +     n =    30

 

.10d + .05n = 2.10

 

Multiply the first equation by -.05 will eliminate the n terms:

 

 -.05d - .05n = -1.50

 

  .10d + .05n =  2.10

------------------------

 

.05d = .60

 

divide both sides by .05:

 

d = 12

 

Using the number of coins equation, we can find the value of n:

 

d + n + 1 = 31

 

Substitute for d:

 

12 + n + 1 = 31

 

13 + n = 31

 

Subtract 13 from both sides:

 

n = 18

 

There are 12 dimes, 18 nickels, and 1 quarter in the coin bank.

 

Check

 

.10 * 12 + .05 * 18 + .25 * 1 = 2.35

 

1.20 + .90 + .25 = 2.35

 

2.35 = 2.35

 

Values check.

 

Questions?