HELP ------ Solve the following problem. It may be helpful to draw a chart on scrap paper to organize the information and write the equation. Be sure to show all steps (V.E.S.T.) and work in order to receive full credit.

A clerk was asked to change a $10 bill. She returned 9 more dimes than nickels and twenty-one more quarters than dimes. How many coins of each did she return?

Question

HELP ------> Solve the following problem. It may be helpful to draw a chart on scrap paper to organize the information and write the equation. Be sure to show all steps (V.E.S.T.) and work in order to receive full credit.



A clerk was asked to change a $10 bill. She returned 9 more dimes than nickels and twenty-one more quarters than dimes. How many coins of each did she return?

anonymous · Answer

Let N be the number of Nickels, D the number of Dimes and Q the number of Quarters. 
Then 5N + 10D + 25Q = 1000 : which is just convertinq the value of each coin so that all together they add up to $10.00 = 1000 cents
But, there are 9 more Dimes than Nickels so D = N + 9.
And, there are 21 more Quarters than Dimes so Q = D + 21. Substituting for D gives Q = N + 9 + 21 = N + 30.
Now substituting for D and Q in the original equation gives :-
5N + 10(N + 9) + 25(N + 30)=5N + 10N + 90 + 25N + 750=40N + 840=1000
40N = 1000 - 840 = 160 therefore N = 160/40 = 4.
As N = 4 then D = 13 and Q = 34.

4 x 5c + 13 x 10c + 34 x 25c = 20 + 130 + 850 = 1000c = $10.00