Question 765394: 3) Aaron has two times as many pennies as nickles. If Aaron had nine more nickles and seven fewer pennies, he would have the same number of each coin. How many money does he have?
7) Jasmine's dimes and nickles total $5.25. If the dimes were replaced by nickles and nickles were replaced by dimes, then she would have $7.50. How many of each coin does she have?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 3) Aaron has two times as many pennies as nickles.
If Aaron had nine more nickles and seven fewer pennies, he would
have the same number of each coin.
How many money does he have?
Let p = no. pennies
Let n = no. of nickels
Write an equation for what it says
"Aaron has two times as many pennies as nickles."
p = 2n
"If Aaron had nine more nickles and seven fewer pennies, he would have the same number of each coin."
n + 9 = p - 7
Replace p with 2n
n + 9 = 2n - 7
9 + 7 = 2n - n
16 = n, sixteen nickels
then
2(16) = 32 pennies
You can check this yourself in the 2nd equation
:
7) Jasmine's dimes and nickles total $5.25.
If the dimes were replaced by nickles and nickles were replaced
by dimes, then she would have $7.50.
How many of each coin does she have?
let x = no. nickels
let y = no. of dimes
Write an equation for each scenario
.05x + .10y = 5.25
.10x + .05y = 7.50
multiply the 1st equation by 2, subtract the 2nd
.10x + .20y = 10.50
.10x + .05y = 7.50
----------------------Subtraction eliminates x, find y
0 + .15y = 3.00
y = 3.00/.15
y = 20 dimes
Find x
.05x + .10(20) = 5.25
.05x = 5.25 - 2
.05x = 3.25
x = 3.25/.05
x = 65 nickels
:
I'll let you check this solution.
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