Question

Jim has 44 nickels and dimes totaling $2.95. How many nickels does he have.

Answer 1

Answer:

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Step-by-step explanation:

Whenever you have this type of question (a question of "how many coins") along with a dollar amount, this will signal that you will have two equations. One equation will total the value of the coins. The second equation will total the number of each coin the person has.

The total value of the coins is $3.10. Let x = number of nickels and y = number of dimes. Since the coins have two different values, you must use two different variables. Assign the appropriate decimal value to each variable: 5 cents for a nickel, 10 cents for a dime.

Equation 1: .05x + .10y = 3.10

The second equation is a quantity equation: how many coins of each does Carter have?

Equation 2: x + y = 37.

.05x + .10y = 3.10

x + y = 37

Now, you need to cancel out one of the variables (either x or y) in order to solve for one.

Let's cancel out the x value first. Do this by multiplying each term in the second equation by -.05

The first equation stays the same.

.05x + .10y = 3.10

-.05x - .05y = -1.85

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Now combine the x terms, y terms and the decimals. You'll notice that .05x and -.05x cancel out, so you are left with

.05y = 1.25

Divide both sides by .05

y = 25

Remember that y is the number of dimes. Carter has 25 dimes.