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Jacob has 1 more twenty-cent coin than one-dollar coin. The total value of the one-dollar coins is $5.40 more than the total value of the twenty-cent coins. How many coins does Jacob have altogether?

 Apr 18, 2021
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Let's say that the number of 20 cent coins is x and the number of dollar coins is y.
Since Jacob has 1 more 20 cent coin:
x=y+1
Then there's also the statement,"The total value of the one-dollar coins is $5.40 more than the total value of the twenty-cent coins."
Since x and y are the number of coints, if we multiply them by the value of each coin we will get to total value of each group of coins.
0.2x + 5.40 = 1y
Let's multiply both sides by ten just to get the decimals out
2x+54=10y
Now we can do substitution. Since x=y+1, let's plug that in. Remember to plug in with parentheses.
2(y+1)+54=10y
2y+2+54=10y
56 = 8y
7 = y

If there are 7 dollar coins, there are 8 20 cent coints so 7+8 = 15 giving us 15 total coins

 Apr 18, 2021

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