SOLUTION: Zachary has one-dollar coins, Jessica has pennies, Jasmine has quarters, Amber has nickels, and Jason has dimes. Jasmine has 11 more coins than Jessica. Jason, Jessica, and Jasmin

Question 590609: Zachary has one-dollar coins, Jessica has pennies, Jasmine has quarters, Amber has nickels, and Jason has dimes. Jasmine has 11 more coins than Jessica. Jason, Jessica, and Jasmine have $7.77 worth of coins. Jason has 7 more coins than Jessica. The value of Amber's coins is worth $29.15 less than the value of Zachary's coins. Zachary has 13 more coins than Amber. How many coins does each student have?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Assign the variables to represent the number of each type of coin
Zachary has one-dollar coins, (c = no. of $))
Jessica has pennies, (p = no. of pennies)
Jasmine has quarters, (q = no. of quarters)
Amber has nickels, and (n = no. of nickels)
Jason has dimes. (d = no. of dimes)
:
Write an equation for each statement using the above variables.
:
Jasmine has 11 more coins than Jessica.
q = p+11
:
Jason, Jessica, and Jasmine have $7.77 worth of coins.
.10d + .01p + .25q = 7.77
:
Jason has 7 more coins than Jessica.
d = p+7
Right here we can use these three equations to find p, substitute for q and d
.10(p+7) + .01p + .25(p+11) = 7.77
.10p + .7 + .01p + .25p + 2.75 = 7.77
.36p + 3.45 = 7.77
.36p = 7.77 - 3.45
.36p = 4.32
p = 4.32/.36
p = 12 pennies (Jessica)
:
The value of Amber's coins is worth $29.15 less than the value of Zachary's coins.
1.00c - .05n = 29.15
:
Zachary has 13 more coins than Amber.
c = n+13
substitute (n+13) for c in the above equation
1(n+13) - .05n = 29.15
.95n = 29.15 - 13
.95n = 16.15
n = 16.15/.95
n = 17 nickels (Amber)
then
q = p+11
q = 12 + 11
q = 23 quarters (Jasmine)
:
d = p + 7
d = 12 + 7
d = 19 dimes (Jason)
and
c = n+13
c = 17 + 13
c = 30 dollar coins (Zachary)
:
:
See if this checks out in the statement;
"The value of Amber's coins is worth $29.15 less than the value of Zachary's coins."
30 - .05(17) =
30 - .85 = 29.15
:
How many coins does each student have? You can answer this now.
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