Algebra!!!! Please help!!! Thanks!!!?

Question

Benjamin has Nickels, dimes, and quarters in his toy bank. He has three times as ,many nickels as dimes and five more quarters than nickels. The coins have a total value of 23.25. How many dimes, nickels, and quarters does he have?

Please show variables,
equation,
and work

Thanks so much!!!!!!!!

Answer 1

The trick to word problems like this is to turn the words into equations

We'll let N, D, and Q stand for the number of nickles, dimes, and quarters.

"He has three times as many nickles as dimes..."

N = 3D or D = 1/3 N

"...and five more quarters than nickles."

Q = N + 5 or N = Q - 5

"The coins have a total value of 23.25"

Q * .25 + D * .10 + N * .05 = 23.25

You now have three equations and three unknowns. To solve, use your first two expressions to write Q and D in terms of N, plug them into the third equation, and solve for N. Then you can get your answers for Q and D. Good luck!

Answer 2

This is the answer written out how we learned. It checks out.:


Let x= the amount of dimes
3x= the amount of nickles
3x+5=the amount of quarters

0.10x+0.05(3x)+0.25(3x+5)=23.25
0.10x+0.15x+0.75x+1.25=23.25
1x+1.25=23.25
-1.25 -1.25
x=22

x=22
3x=66
3x+5=71

Benjamin has 22 dimes, 66 nickles and 71 quarters in his toy bank.