Question

Your piggy bank has a total of 46 coins in it; some are dimes and some are quarters. If you have a total of $7.00, how many quarters and how many dimes do you have? (please explain to me. I'm not great with systems of equations.)

Answer 1

You know you have 46 coins, and you have dimes and quarters. The total of the dimes and quarters needs to add up to 7 dollars. The systems of equations should be:

0.1d + 0.25q = 7
d + q = 46

does this help? (:

Answer 2

should have mentioned this as well:

the first equation shows that 0.1d (the total amount from the dimes) plus 0.25q (the total amount from te quarters) should equal 7 dollars.

the second equation shows that the number of dimes and quarters must add up to 46 coins.

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After this, you shold solve for either d or q. Let's say you were to solve for q, quarters. You multiply the second equation by -0.1 (negative, because we need to cancel out the d variable).

-0.1 (d + q = 46) --> -0.1d - 0.1q = -4.6

So our equations are now:

0.1d + .25q = 7
-0.1d - 0.1q = -4.6

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Now add both of the equations. You can cancel 0.1d and -0.1d, leaving you with:

.24q = 2.4

divide both sides by .24:

q = 10

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So there are 10 quarters. With this information, you can solve for d, the number of dimes

Hope this helped!! C;

Answer 3

It's a bit hard to understand the work but I think I kind of get it.