SOLUTION: I am stuck on this question!! Sam has some quarters, nickels, and dimes. He has 4 more quarters than dimes and 3 more dimes than nickels. If n represents the number of nickels

Question 478795: I am stuck on this question!!
Sam has some quarters, nickels, and dimes. He has 4 more
quarters than dimes and 3 more dimes than nickels. If n
represents the number of nickels he has, which of the
following represents, in cents, the total value of all his
coins?
A. 40n + 205
B. 40n + 130
C. 40n + 7
D. 7n + 130
E. 3n + 10
Found 2 solutions by Tatiana_Stebko, Theo:
Answer by Tatiana_Stebko(1539) (Show Source): You can put this solution on YOUR website!
If represents the number of nickels he has, then he has dimes, and quarters.
The total value of all his coins is
Answer: A.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i get 40n + 205
we can test to see if this is accurate.
first we'll solve.
n = number of nickels.
d = number of dimes
q = number of quarters
he has 4 more quarters than dimes.
this leads to the equation:
q = d + 4
he has 3 more dimes than nickels
this leads to the equation:
d = n + 3
since d = n + 3 and q = d + 4, this means that:
q = (n+3)+4 which leads to:
q = n+7
so we have:
d = n + 3
q = n + 7
now we need to get to the value equation.
a quarter is worth 25 cents, so we multiply the number of quarters by 25 to get their value in cents.
a dime is worth 10 cents, so we multiply the number of dimes by 10 to get their value in cents.
a nickel is worth 5 cents, so we multiply the number of nickels by 5 to get their value in cents.
the total value of our money is:
25q + 10d + 5n
since q is equal to n+7 and d is equal to n+3, we can replace q and d in this equation to get:
25(n+7) + 10(n+3) + 5n
simplify this to get:
25n + 175 + 10n + 30 + 5n
combine like terms to get:
40n + 205
that's the value of our money.
now let's see if this equation makes sense.
suppose we have 100 nickels.
the total value of our money should be:
40*100 + 205 = 4205 cents
we are saying that 25q + 10d + 5n = 4205
n = 100
d = n+3 = 103
q = d+4 = 107
25(107) + 10(103) + 5(100) should be equal to 4205 if everything is copacetic.
multiplying these out gets us:
2675 + 1030 + 500 = 4205
the value of the money equals the same whether we used the initial equation or the final equation so we're good.
your answer is:
40n + 205 (selection A)

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