Joe has nickels & dimes worth 7.65. If the the dimes were doubled and the nickels increased by 35, the value would be 14.30.  How many nickels and dimes were there initially?Must show work.

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mlsiasebs | College Teacher | (Level 1) Associate Educator

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Since we have two unknowns, we need to assign variables to each of them.

x = number of nickels

y = number of dimes

Given the initial information, we know that

x(0.05) + y(0.10) = 7.65

Since we have two unknowns, we need a second equation.  We can do this with the information given in the problem for the second total.

The dimes are doubled so we can change that to 2y.  The number of nickels is increased by x + 35 and write a new equation

(x+35)(0.05) + 2y(0.10) = 14.30

Using the first equation we can solve for x

x(0.05) + y(0.10) = 7.65

0.05x = 7.65-0.10y

x = 153 - 2y

Now, we can substitute the value for x into the second equation

(x+35)(0.05) + 2y(0.10) = 14.30

(153-2y+35)(0.05) + 2y(0.10) = 14.30

Once we get this, it's just a matter of doing the algebra to work out the value of y.

(188-2y)(0.05) + 2y(0.10) = 14.30

9.4 - 0.10y + 0.2y = 14.30

9.4 + 0.1y = 14.30

0.1y = 4.90

y = 49

Since we assigned y as the number of dimes, we know that we have 49 dimes.  Now we can subsitute y into either of the equations to solve for x.

x(0.05) + y(0.10) = 7.65

x(0.05) + 49(0.10) = 7.65

0.05x = 2.75

x = 55 nickels

We can check our answer by putting both the x and y values into the second equation

(x+35)(0.05) + 2y(0.10) = 14.30

(55+35)(0.05) + 2(49)(0.10) = 14.30

90(0.05) + 98(0.10) = 14.30

4.50 + 9.80 = 14.30

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