The system of equation is:
x + y = 20
x - y = 4
She has 12 dimes and 8 nickels
Step-by-step explanation:
The given is:
We need to write a system of equations that represents the problem and how
many of each coin she has
Assume that she has now x dimes and y nickels
∵ She has x dimes and y nickels
∵ She has a total of 20 coins
- Add x and y, then equate the sum by 20
∴ x + y = 20 ⇒ (1)
∵ One dime = 10 cents
∵ One nickels = 5 cents
- Multiply x by 10 and y by 5 to find how many cents she has now
∵ She has now (10x + 5y) cents
∵ The dimes were nickels and the nickels were dimes
- Multiply x by 5 and y by 10 to find how many cents she has
after the change
∴ She had after the change (5x + 10y) cents
∵ The value after the change is less than the value now by
20 cents
- Subtract (5x + 10y) from (10x + 5y) and equate the difference
by 20
∴ (10x + 5y) - (5x + 10y) = 20
- Add the like terms in the left hand side
∴ (10x - 5x) + (5y - 10y) = 20
∴ 5x - 5y = 20
- Divide both sides by 5
∴ x - y = 4 ⇒ (2)
The system of equation is:
x + y = 20
x - y = 4
Now we have a system of equations to solve it
Add equations (1) and (2) to eliminate y
∴ 2x = 24
- Divide both sides by 2
∴ x = 12
- Substitute the value of x in equation (1) to find y
∵ 12 + y = 20
- Subtract 12 from both sides
∴ y = 8
She has 12 dimes and 8 nickels
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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