Question 1097683

In a purse Misty has 1.91, including one more nickel than quarters. She also has twice as many dimes as nickels. But, she also has eight more pennies than dimes. How many of each of the four coins does Misty have?

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So what I did was use the formula: Quantity X Value = Subtotal.
<pre>Only <b><u>ONE VARIABLE</b></u> is needed, and that's Q for the number of quarters
Then number of nickels = Q + 1
Number of dimes: 2(Q + 1), or 2Q + 2
Number of pennies: 2Q + 2 + 8, or 2Q + 10
We then get: .25Q + .05(Q + 1) + .1(2Q + 2) + .01(2Q + 10) = 1.91
.25Q + .05Q + .05 + .2Q + .2 + .02Q + .1 = 1.91
.25Q + .05Q + .2Q + .02Q + .05 + .2 + .1 = 1.91 
.52Q + .35 = 1.91
.52Q = 1.56
{{{highlight_green(matrix(1,9, Q, or, number, of, quarters, "=", 1.56/.52, "=", 3))}}}
{{{highlight_green(matrix(3,6, Number, of, "nickels:", 3 + 1, "=", 4,  Number, of, "dimes:", 2(3) + 2, "=", 8, Number, of, "pennies:", 2(3) + 10, "=", 16))}}}