SOLUTION: Can someone please help me im stuck?
9. Sandy has $3.75 in change. She has three more quarters than dimes but twice as many nickels as quarters. Express the given information as
Algebra.Com
Question 151661This question is from textbook elementary and intermediate algebra concepts and applications
: Can someone please help me im stuck?
9. Sandy has $3.75 in change. She has three more quarters than dimes but twice as many nickels as quarters. Express the given information as an algebraic expression and simplify. [You are not required to solve the problem]
This question is from textbook elementary and intermediate algebra concepts and applications
Answer by mducky2(62) (Show Source): You can put this solution on YOUR website!
In order to set up the equation, you must multiply the value of each coin times the number of each coin and add it up. Although we know the value of each coin, we only know the proportions of the amount of each coin. We can label the number of coins:
Number of quarters: q
Number of dimes: d
Number of nickels: n
Multiplying the values of each should come out to be:
25q + 10d + 5n = 375
However, we can't solve this equation until we only have one variable.
Because we know the proportions, we can solve for ratios of each coin in terms of each other. Both ratios include quarters, so let's solve for the amounts in terms proportion. Since there are three more quarters than dimes, we can solve for dimes in terms of quarters:
q = d + 3
d = q - 3
Since there are two times as many nickels as there are dimes, we can set up the equation:
n = 2q
Plugging this into the original equation above:
25q + 10d + 5n = 375
25q + 10(q-3) + 5(2q) = 375
25q + 10q - 30 + 10q = 375
45q = 375 + 30
45q = 405
q = 9
Sandy has nine quarters.
Now we can plug that into the other equations:
d = q - 3
d = 9 - 3
d = 6
n = 2q
n = 2(9)
n = 18
Therefore, Sandy has 9 quarters, 6 dimes, and 18 nickels.
RELATED QUESTIONS
Hi. I need help answering the following question. Thanks in advance.
Sandy has $3.75 in... (answered by nerdybill)
I need help with this word problem. Can anyone help me? I do appreciate whatever you can... (answered by ankor@dixie-net.com,scott8148)
Sandy has $3.75 in change. She has three more quarters than dimes but twice as many... (answered by ankor@dixie-net.com)
Sandy has $3.75 in change. She has three more quarters than dimes but twice as many... (answered by jojo14344)
sandy has $3.75 in change. she has three more quarters than dimes but twice as many... (answered by ankor@dixie-net.com)
Sandy has $3.75 in change. She has 3 more quarters than dimes but twice as many nickles... (answered by jojo14344)
Sandy has 3.25 in change. She has five more dimes than quarters but twice as many nickels (answered by Mathtut)
sandy has $3.25 in change. She has five more dimes than quarters but twice as many... (answered by ankor@dixie-net.com)
Sandy has $3.25 in change. She has five more dimes than quarters but twice as many... (answered by solver91311)