A purse contains $3.73 in pennies and nickels. If the number of pennies was halved and the number of nickels was doubled, the money would amount to $7.04. How many nickels were there originally?
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A purse contains $3.73 in pennies and nickels. If the number of pennies was halved and the number of nickels was doubled, the money would amount to $7.04. How many nickels were there originally?
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Answer:
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Step-by-step explanation:
Let's start by setting up equations for the given information:
Let x be the number of pennies.
Let y be the number of nickels.
From the first statement, we know that:
0.01x + 0.05y = 3.73
From the second statement, we can create a new equation with the changes:
0.01(x/2) + 0.05(2y) = 7.04
0.005x + 0.1y = 7.04
We now have two equations with two variables, so we can solve for x and y.
First, let's simplify the second equation by multiplying everything by 100 to eliminate decimals:
0.5x + 10y = 704
Now we can use the first equation to solve for x in terms of y:
0.01x + 0.05y = 3.73
0.01x = 3.73 - 0.05y
x = (3.73 - 0.05y)/0.01
x = 373 - 5y
We can substitute this expression for x into the second equation and solve for y:
0.5x + 10y = 704
0.5(373 - 5y) + 10y = 704
186.5 - 2.5y + 10y = 704
7.5y = 517.5
y = 69
Therefore, there were originally 69 nickels.