If I have 35 dimes and quarters that equal 5 dollars how many dimes and how many quarters do I have?

Question

I don't understand this and it bothers me that i and my family can't figure it out

Answer 1

This question acts as a linear pair equations. Let's first start off with IDing our variables:

d = dimes, q = quarters.

Here's what we know:

d + q = 35 (you have 35 coins in dimes and quarters together)

.1d + .25q = 5 (the change total is $5)

 

As a linear pair, there are two common methods to solve--we can use substitution by taking the first equation and isolating one of the variables to put into the second equation.

The other way is elimination. By multiplying the entirety of one or both equations by values so that we can get rid of one variable, we can focus on solving the other, which I'll use in this case.

 

-4(.1d + .25q = 5) ⇒ -.4d - q = -20

 

Now I can eliminate q by subtracting one equation from the other:

 

  d  + q =  35

-.4d - q = -20

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

.6d = 15

 

Now we isolate d by dividing both sides by .6 (which is the same as multiplying both sides by 10/6):

15 * 10/6  ⇒  15 * 5/3  ⇒  5 * 5 = 25

(10 and 6 have a 2 in common to cancel. 15 and 3 have a 3 in common to cancel.)

d = 25

 

Now that we know the number of dimes, we can solve for quarters:

25 + q = 35

Subtract 25 from both sides:

q = 10

 

Let's check our answer:

.1 * 25 + 10 * .25 = 5

2.5 + 2.5 = 5

5 = 5

Answer 2

Let x be your quarter number and 35 - x be your dime number

 

.25x +.10(35-x) = 5                               Multiply each by the money's value Q = .25, D = .10

.25x + 3.5 - .10x = 5                             Solve for x

.15x + 3.5 = 5

.15x = 1.5

x = 10 Quarters

35 - 10 = 25 Dimes

 

So your answer turns to be 10 Quarters and 25 Dimes.