MHB How many dimes does Ginger have?

[mathdad]

Ginger has 15 quarters and dimes. The total is $2.55. How many dimes does she have?

Let q = quarters

Let d = dimes

0.15q +0.10d = 2.55
q + d = 15

Is this the correct set up?

 

[MarkFL]

Ginger has 15 quarters and dimes. The total is $2.55. How many dimes does she have?

Let q = quarters

Let d = dimes

0.15q +0.10d = 2.55
q + d = 15

Is this the correct set up?

I would bet big money that it's just a typo, but what you want is:

0.25q +0.10d = 2.55
q + d = 15

But otherwise, your methodology is spot on. :D

 

[mathdad]

I would bet big money that it's just a typo, but what you want is:

0.25q +0.10d = 2.55
q + d = 15

But otherwise, your methodology is spot on. :D

Cool. Take a look at the other question about to be posted.

 

[MarkFL]

Cool. Take a look at the other question about to be posted.

I would multiply the first equation by 20, and the second equation by -5, then add them together, which will eliminate q, at which point you can solve for d to answer the question. ;)

 

[mathdad]

8 + 7 = 15

7(0.25) = 1.75

2.55 - 1.75 = 0.80

0.80/0.10 = 8

Answer: 8 dimes

Correct?

 

[MarkFL]

8 + 7 = 15

7(0.25) = 1.75

2.55 - 1.75 = 0.80

0.80/0.10 = 8

Answer: 8 dimes

Correct?

Yes, when I did what I suggested above, I got:

$$5q+2d=51$$

$$-5q-5d=-75$$

Adding the equations, we get:

$$-3d=-24$$

$$d=8\quad\checkmark$$

 

[mathdad]

Yes, when I did what I suggested above, I got:

$$5q+2d=51$$

$$-5q-5d=-75$$

Adding the equations, we get:

$$-3d=-24$$

$$d=8\quad\checkmark$$

Nicely done.