contestada

A charity organization is collecting change to raise money. They have collected three times as many dimes as quarters, 11 more nickels than dimes, and 2 times as many pennies as nickels. If they have collected a total of 4453 coins, how many of each coin have they collected?

Respuesta :

Answer:they collected 1020 dimes, 340 quarters, 1031 nickels and 2062 pennies.

Step-by-step explanation:

Let d represent the number of dimes that they collected.

Let q represent the number of quarters that they collected.

Let n represent the number of nickels that they collected.

Let p represent the number of pennies that they collected.

They have collected three times as many dimes as quarters. It means that

d = 3q

q = d/3

The collected 11 more nickels than dimes. It means that

n = 11 + d

They collected 2 times as many pennies as nickels. It means that

p = 2n

p = 2(11 + d)

p = 22 + 2d

If they have collected a total of 4453 coins, it means that

p + q + d + n = 4453 - - - - - - - - - -1

Substituting q = d/3, n = 11 + d and

p = 22 + d into equation 1, it becomes

22+ 2d + d/3 + d + 11 + d = 4453

66 + 6d + 6d + d + 33 = 13359

13d = 13359- 99

13d = 13260

d = 13260/13

d = 1020

q = d/3 = 1020/3

q = 340

n = 11 + d = 11 + 1020

n = 1031

p = 22 + 2d = 22 + 2 × 1020

p = 2062

Otras preguntas