Question

The value of Ari's rolls of coins is $113.00. If pennies and dimes come in rolls of 50 coins each, and nickels and quarters come in rolls of 40 coins each, which of these combinations could Ari have?

A. 5 rolls of pennies, 8 rolls of nickels, 4 rolls of dimes, and 7 rolls of quarters
B. 4 rolls of pennies, 8 rolls of nickels, 7 rolls of dimes, and 5 rolls of quarters
C. 4 rolls of pennies, 8 rolls of nickels, 5 rolls of dimes, and 7 rolls of quarters
D. 5 rolls of pennies, 8 rolls of nickels, 7 rolls of dimes, and 4 rolls of quarters

Answer 1

Option C is correct.

Explanation:

Given is :

The value of Ari's rolls of coins is = $113

The coins are pennies, dimes, nickels and quarters.

Total money is represented by = penny + nickle + dime + quarter All values in dollars are represented by:

113 = .01* pennies + .05* nickles + 0.1* dimes + 0.25* quarters

Further calculating we get,

113 = .01* 50*penny rolls + .05 * 40*nickle rolls + .1 * 50*dime rolls + .25 * 40*quarter rolls

`113=.5p+2n+5d+10q`

where p is the number of penny rolls, n is the number of nickle rolls, d is the number of dime rolls, and q is the number of quarter rolls

Now checking all the options by putting values.

A.
`113=.5(5)+2(8)+5(4)+10(7)`

`113\\eq 108.5`

B.
`113=.5(4)+2(8)+5(7)+10(5)`

`113\\eq 103`

C.
`113=.5(4)+2(8)+5(5)+10(7)`

`113=113`

D.
`113=.5(5)+2(8)+5(7)+10(4)`

`113\\eq 93.5`

Therefore, option C is the right option.

Answer 2

An odd number of rolls of pennies ($0.50 each) cannot be part of the solution, making answers A and D not worthy of consideration.

The correct choice is C.