A bag contains 39 coins consisting of quarters and nickels the total value of the coins is $6.35 which system of equation can be used to used to determine the number of quarters Q and the number of nickels n In the bag

The system of equation to determine the quantity of nickels and quarters is simultaneous equation.

Nickels = 17

Quarters = 22

Step-by-step explanation:

Given

Let n represent number of nickels

Let q represent number of quarters

From line 1 of the question, we understand that

Total coins = 39

So, n + q = 39 because the made up of the nickels and the quarters

It's also stated that the total value of these 39 coins is $6.35.

First, it should be noted that

1 nickel is worth 0.05 and 1 quarter is worth 0.25, we can represent the total value of the coins with the following equation

0.05n + 0.25q = 6.35

At this point, we have two equation such can be solved simultaneously

n + q = 39 (1)

0.05n + 0.25q = 6.35 (2)

So, the system of equation to determine the quantity of nickels and quarters is simultaneous equation.

Solving further

Make q the subject of formula in equation (1)

q = 39 - n

Substitute 39 - n for q in equation 2

0.05n + 0.25q = 6.35 becomes

0.05n + 0.25(39 - n) = 6.35

0.05n + 9.75 - 0.25n = 6.35

Collect like terms

0.05n - 0.25n = 6.35 - 9.75

-0.2n = -3.4

Divide through by -0.2

-0.2n/-0.2 = -3.4/-0.2

n = 17

Recall that q = 39 - n

Substituton 17 for n in this equation

q = 39 - 17

q = 22

Hence, there are 17 nickels and 22 coins

22

step-by-step explanation: