177k views
3 votes
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

1 Answer

2 votes

Answer:

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

Nickels = 17

Quarters = 22

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

User Vovkas
by
9.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.