Question

Marcos had 15 coins in nickels and quarters. He had 3 more quarters than nickels. He wrote a system of equations to represent this situation, letting x represent the number of nickels and y represent the number of quarters. Then he solved the system by graphing.What is the solution?

Answer 1

Answer:

There are 6 coins in nickels and 9 coins in quarters.

Step-by-step explanation:

Now, to find the solution.

According to question:

The number of nickels = $x$.

The number of quarters = $y.$

So, the total number of coins:

$x+y=15.$

He had 3 more quarters than nickels.

Thus,

$y=x+3$ .....(1)

Now, to get the solution:

$x+y=15$

Substituting the equation (1):

$x+(x+3)=15$

$x+x+3=15$

$2x+3=15$

Subtracting both sides by 3 we get:

$2x=12$

Dividing both sides by 2 we get:

$x=6.$

The number of nickels = 6.

Now, substituting the value of $x$ in equation (1):

$y=x+3\\\\y=6+3\\\\y=9.$

The number of quarters = 9.

Thus, there are 6 coins in nickels and 9 coins in quarters.