SOLUTION: Solve the problem and show the equation used for the solution. Jill has $3.50 in nickels and dimes. If she has 50 coins how many of each coin does she have?

Question 68531: Solve the problem and show the equation used for the solution. Jill has $3.50 in nickels and dimes. If she has 50 coins how many of each coin does she have?
Answer by rmromero(383) (Show Source): You can put this solution on YOUR website!
Jill has $3.50 in nickels and dimes. If she has 50 coins how many of each coin does she have?
What is asked in the problem?
How many coins does she have?

Given:
1. she have $3.50 in nickels and dimes
2. She has 50 coins.

Representation:
Let x = number of dimes
y = number of nickels
Translate the given sentences to mathematical equation using x and y.

She has 50 coins. Number of Dimes + Number of Nickels = 50 ---> x + y = 50
She have $3.50. Dime = 10cents, Nickel = 5 cents.
0.10x + 0.05y = $3.50. You can multiply 100 each term so that we wont deal with decimals. 10x + 5y = 350

Solve the systems of equation:
x + y = 50
0.10x + 0.05y = $3.50

x + y = 50
10x + 5y = 350

Multiply -5 to x + y = 50
-5x - 5y = -250
10x + 5y = 350

Add
5x = 100 , divdide both sides by 5 to solve for x
x = 20

Find y by substituting x = 20 to either of the two equations.
x + y = 50 , x = 20
20 + y = 50
y = 30
Checking
x + y = 50
20 + 30 = 50
50 = 50 ------------->> True
.10x + .05y = $3.50
.10(20) + .05(30) = 3.50
2.00 + 1.50 = 3.50
3.50 = 3.50 --------->> True

Therefore She has 20 Dimes and 30 Nickels.

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