) A coin collection consisting of pennies, dimes, and quarters totals 45 coins. The number of quarters is five more than twice the number of pennies and the number of dimes is four
more than the number of pennies. How much is the coin collection worth?/

9514 1404 393

  $7.14

Step-by-step explanation:

Let p, d, q represent the numbers of pennies, dimes, and quarters in the collection, respectively.

  p + d + q = 45 . . . . . . . . there are 45 coins in the collection

  2p +5 = q . . . . . . . . . . . . 5 more than twice the number of pennies

  p + 4 = d . . . . . . . . . . . . . 4 more than the number of pennies

Substituting the last two equations into the first gives ...

  p +(p +4) +(2p +5) = 45

  4p = 36 . . . . . . . . . . . . . subtract 9

  p = 9 . . . . . . . . . . . divide by 4

  d = 9 +4 = 13

  q = 2(9) +5 = 23

The value of the collection is ...

  23(0.25) +13(0.10) +9(0.01) = 5.75 +1.30 +0.09 = 7.14

The coin collection is worth $7.14.

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9