Layla emptied out her change jar to buy a new binder for school. She found 147 coins consisting of dimes and nickels that totaled $11.65. Write a system of equations that could be used to determine how many dimes, d, and how many nickels, n, Layla had in her change jar.

d + n = 147

0.10d + 0.05n = 11.65

d = 86, n = 61

Step-by-step explanation:

Let

Number of dimes = d

Number of nickels = n

Total coins = 147

Total value = $11.65

d + n = 147 (1)

0.10d + 0.05n = 11.65 (2)

From (1)

d = 147 - n

Substitute d = 147 - n into

0.10d + 0.05n = 11.65

0.10(147 - n) + 0.05n = 11.65

14.7 - 0.10n + 0.05n = 11.65

- 0.10n + 0.05n = 11.65 - 14.7

-0.05n = -3.05

n = -3.05 / -0.05

= 61

n = 61

Substitute n = 61 into

d + n = 147

d + 61 = 147

d = 147 - 61

d = 86