Without actually solving the problem, choose the correct solution by deciding which choice satisfies the given conditions.

Question

Keisha has a total of 80 coins, all of which are either dimes or quarters. The total value of the coins is $11.00. Find the number of each type of coin.

Answer 1

Hi Certis,

 

Let number of dimes be x, number of quarters be y.

 

Total number of coins are 80 so

 

x+y= 80....... eq 1

10x+25y=1100...... eq 2

divide eq 2 by 5, we get,

 

2x+5y=220 ... ....    eq 3

 

now multiply eq 1 by 2 so we get,

 

2x+2y=160........eq 4

 

subtract eq 4 from eq 3,

 

2x+5y=220

-2x-2y=-160

    3y = 60

y= 20

 

x=60

Number of dimes=60, Number of quarters= 20

Check your answer,20 quarters= $5 , 60 dimes= $6

                                Total $11.

 

 

 

 

Answer 2

D is the number of dimes

Q is the number of quarters

 

We are given two equations to start off with.  First, we know the number of coins total, so:

1) D + Q = 80

 

 

Secondly, we know the total value of the coins, so if we multiply the number of dimes by 10 cents and the number of quarters by 25 cents, we should get 1100 cents, so

2) 10D + 25Q = 1100

 

Multiply equation 1 by 10

10D + 10Q = 800

 

The subtract equation 1 from the equation 2.

15Q = 300

 

Then solve for Q:

Q = 20  (So there are 20 quarters)

 

Then go back and solve for D:

D = 80 - Q (based on equation 1), so

D = 80 - 20 = 60 (So there are 60 dimes)

 

Now check your work:

We can confirm this by using equation 2

10*60 + 25*20 = 1100, and that checks out.

 

Hope this helps, Curtis!