You can write three equations in the numbers of nickels (n), dime (d), and quarters (q).
n + d + q = 23 . . . . . . . there are 23 coins total
0n +d -q = 2 . . . . . . . . .there are 2 more dimes than quarters
5n +10d +25q = 250 . .the total value is $2.50
The collection includes 11 nickels, 7 dimes, and 5 quarters.
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I used the matrix function of my calculator to solve these equations. You can find q by subtracting from the last equation five times the sum of the first two equations.
(5n +10d +25q) -5((n +d +q) +(d -q)) = (250) -5(23 +2)
25q = 125 . . . . . . . simplify
q = 5
From the second equation,
d = q +2 = 7
And from the first,
n = 23 -5 -7 = 11
The answer to the question
In order to get the common denominator when adding fractions or subtracting fractions, you have to make sure that the denominator of the two items are divisible by each other. In this case, 9 is not divisible by any of the given denominators which is 4 and 5. So in this case, the common denominator will have to be 20. 5 x 4 will equal to 20 and you will also multiply 3 x 5 to get the new numerator. After that, you will multiply 2 x 4 to get the new numerator of the other fraction. The new fractions will be 15/20 and 8/20. From there, you can add or subtract
YES
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A i think
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