emma paid the $11.17 bill for her lunch with 244 coins consisting of pennies, nickels, and dimes. if the…

emma paid the $11.17 bill for her lunch with 244 coins consisting of pennies, nickels, and dimes. if the number of nickels plus the number of dimes was equal to the number of pennies, then how many coins of each type did she use? she used 122 pennies, 87 nickels, and 35 dimes.

emma paid the $11.17 bill for her lunch with 244 coins consisting of pennies, nickels, and dimes. if the number of nickels plus the number of dimes was equal to the number of pennies, then how many coins of each type did she use? she used 122 pennies, 87 nickels, and 35 dimes.

Answer

Explanation:

Step1: Set up equations based on the problem

Let (p) be the number of pennies, (n) be the number of nickels, and (d) be the number of dimes. We know that:

  1. (p + n + d=244) (total number of coins)
  2. (n + d=p) (given relationship)
  3. (0.01p+0.05n + 0.01d=11.17) (total value of coins)

Substitute (p=n + d) into (p + n + d=244), we get ((n + d)+n + d=244), which simplifies to (2(n + d)=244), so (n + d = 122), and (p=122)

Step2: Substitute (p = 122) into the value equation

Substitute (p = 122) into (0.01p+0.05n + 0.01d=11.17), we have (0.01\times122+0.05n+0.01d=11.17) (1.22+0.05n + 0.01d=11.17) (0.05n+0.01d=11.17 - 1.22=9.95) Since (d=122 - n), substitute (d) into (0.05n+0.01d=9.95) (0.05n+0.01(122 - n)=9.95) (0.05n+1.22-0.01n=9.95) (0.04n=9.95 - 1.22) (0.04n=8.73) (n=\frac{8.73}{0.04}=87)

Step3: Find the number of dimes

Since (n + d=122) and (n = 87), then (d=122 - 87=35)

Answer:

She used (122) pennies, (87) nickels, and (35) dimes.