Let n = number of nickels.
Let d = number of dimes.
Let q = number of quaraters.
n + d + q = ____
5n + 10d + 25q = 450 (Why?)
d = n + 7 (Why?)
Rewrite the first to equations but use (n + 7) everywhere you see d.
n + (n + 7) + q = ???
5n + 10(n + 7) + 25q = 450
You have 2 equations with 2 variables and you should now be able to solve using methods you have learned for solving a "system" of equations. Or you could try graphing the lines that the equations represent and see where the lines cross.
Another way is to think about all the ways that you could have 40 coins and yet have 7 more dimes than nickels:
n d q
0 7 33
1 8 31
2 9 29
3 10 27
4 11 25
5 12 23
You could calculate the value of each set of coins until you find the one that has a value of $4.50. That would be the 'brute force' method! I'm guessing you don't really have that many quarters, so it might be better to start looking later in the list.
Another thing to think about: the list shows that number of quarters must be odd. So total value from quarters will end in 5 cents (.25, .75, 1.25, etc.). No matter how many dimes you have, their value will end in zero (.10, .20, .30), so to get a value of $4.50, you will need to have an odd number of nickels to 'cancel out' the 5 cents in the value of the quarters.
So I'm guessing the answer will have an odd number of nickels, an odd number of quarters, and an even number of dimes. That also helps you cut down the list.
Answer this Question
Math - Dave has quarters, dimes and nickles in his bank. He has 3 more dimes ...
Math - Raul says he has equal numbers of dimes and quarters and four times as ...
Math - a piggy bank contains $8.80 in quarters, dimes and nickles. there are two...
MATH (PLease HELp) - Sally has three times as many dimes as nickels and twice as...
math - you have 40 coins, quarters dimes and nickles and they equal $6.00. you ...
math - greg has 2 quarters, 1 dime, and 3 nickles. Stan has 3 quarters, 2 dimes...
intermediate algebra - joe has a collection of nickles and dimes that is worth $...
math- word problems - I tried doing this problem but i just dont get it: A boy ...
word problem money - you have $ 1.55 in dimes and quarters. find all the ...
3rd grade - My son has this Math word problem and I can come up with the answer ...