Number of Dimes and Quarters

[harpazo]

There are 23 coins in a bank. All the coins are dimes and quarters. The total value of the coins is $3.80. How many dimes are there? How many quarters?

Solution:

I'm interested in the set up.

Let d = dimes
Let q = quarters

d + q = 23
0.10d + 0.25q = 3.80

Is this correct?

 

[Dr.Peterson]

The only quibble I have is that you mean

Let d = number of dimes
Let q = number of quarters

(The variables are both numbers, not pieces of metal.)

Otherwise it's good. (And my comment pertains mostly to communicating with others, like us, rather than to notes you make for yourself -- though there are times when you can misinterpret what you yourself wrote down!)

 

[pka]

This might help you to check your work.

 

[harpazo]

The only quibble I have is that you mean

Let d = number of dimes
Let q = number of quarters

(The variables are both numbers, not pieces of metal.)

Otherwise it's good. (And my comment pertains mostly to communicating with others, like us, rather than to notes you make for yourself -- though there are times when you can misinterpret what you yourself wrote down!)

Rushing through the post is the reason for the slight error.

 

[harpazo]

This might help you to check your work.

I could have completed the thread but the main problem for me has been the set up. I have been struggling with the set up of word problems since the middle school years.

 

[Otis]

Rushing … is the reason for the slight error.

Slow and steady is best, for all of us. (You're not under a deadline, so there's no reason to rush.) If you can, remember to review steps, as you complete them. Pretend your steps are for explaining the solution process to somebody else; check with yourself regularly, and ask whether you think they would understand what you've written.

?

 

[harpazo]

Slow and steady is best, for all of us. (You're not under a deadline, so there's no reason to rush.) If you can, remember to review steps, as you complete them. Pretend your steps are for explaining the solution process to somebody else; check with yourself regularly, and ask whether you think they would understand what you've written.

?

Let d = number of dimes
Let q = number of quarters

d + q = 23.....A
0.10d + 0.25q = 3.80.....B

Solve A for either d or q.

d = 23 - q

Plug into B to find q.

0.10(23 - q) + 0.25q = 3.80

I got q = 10.

Plug q = 10 into EITHER A or B to find d.

d + 10 = 23

d = 23 - 10

d = 13

The number of dimes is 13 and the number of quarters is 10.