MATH SOLVE

4 months ago

Q:
# whitney has a coin jar with a small collection of nickels and dimes. there are 69 coins in the jar. they have a value of $5.90. how many nickels and dimes are in the jar? use substitution to solve.

Accepted Solution

A:

Answer:The number of nickels in the jar is 20.The number of dimes in the jar is 49.Step-by-step explanation:Let us assume the total number of nickels = xThe total number of dimes = yTotal coins = 69 coins ⇒x + y = 69 Now as we know: 1 Nickel = $0.05and 1 Dime = $0.10⇒ The value of x nickels = x ( $0.05) = 0.05 xand The value of y nickels = y ( $0.10) = 0.10 yTotal amount in jar = $5.90 ⇒0.05 x + 0.10 y = $5.90So, the given system of equation isx + y = 69 .............. (1)0.05 x + 0.10 y = 5.90 ....... (2)Substitute the value of y = 69 - x in (2) , we get:0.05 x + 0.10 y = 5.90 ⇒ 0.05 x + 0.10 ( 69 - x) = 5.90or, 0.05 x + 6.9 - 0.10 x = 5.90or, - 0.05 x = -1.00⇒ x = 1/0.05 = 20, or x = 20⇒ y = 69 - x = 69 - 20 = 49Hence the number of nickels in the jar is 20and the number of dimes in the jar is 49.