The value of the number of dimes is equal to the value of the number of quarters. If the total value of the quarters and dimes is $6.00, find the total number of coins.
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25x=10y, so 25x-10y=0
25x+10y=600 if we are working in cents
You can eliminate the 10y from the equations, and you are left with 50x=600, meaning you have 12 quarters. To find the number of dimes (30), simply substitute back into the original equation.
The total number of coins would be 42, and the in between step that i didn't show is this:
by adding these two equations, you get 50x=600
Thank you colette. Can you break this down so that a 6th grader can underdstand? My teacher is away and the sub did not explain how to do this
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Sure thing. Let x be the number of quarters, and let y be the number of dimes. We are going to work in cents to simplify the problem and to not have to work in decimals. The first equation you create will express that (25 cents times the number of quarters) will equal (10 cents times the number of dimes). Do you follow so far?
*25 cents TIMES the number of quarters will give you how much all the quarters are worth, and 10 cents TIMES the number of dimes will give you how much all the dimes are worth, and those two values have to equal each other. Therefore, 25x=10y
Next equation... 25 cents times the number of quarters, plus 10 cents times the number of dimes will have to equal 600 cents. 25x+10y=600
Have you learned elimination yet?
Hmmm... have you learned how to substitute to solve two equations with two variables?
Wonderful! okay... so to do that for this problem, isolate for x with the easier equation, so you would get 10y/25=x. You take that value for x and substitute it in the second equation, and you eventually get y equals 30. (y being the number of dimes).