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):
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)
|
|
|
