Question

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Manny has 85 cents in nickels and dimes. He has 10 coins altogether. The equations at the right relate the number of nickels, x, and the number of dimes, y. How many nickels and how many dimes does Manny have?

Equations: $x+y=10$ and $5x+10y=85$

Answer 1

Answer:

x = 3 which means he has 3 nickels

y = 7 which means he has 7 dimes

Step-by-step explanation:

5x + 10y = 85

x + y = 10

-5 (x + y = 10) Multiply equation by -5 to delete the x's

-5x -5y = -50

5x + 10y = 85   Subtract the new equation from the 2nd equation

         5y = 35

           y = 7

x + 7 = 10

x = 3  

x = 3 which means he has 3 nickels

y = 7 which means he has 7 dimes

Answer 2

Answer:

Step-by-step explanation:

Before getting to solve the two equations: x+y=10 and 5x+10y=85, we look at how we get them.

Let the number of nickels be x, and the number of dimes be y.

Manny has 85 cents in nickels and dimes. Nickels are 5-cent each and dimes are 10-cent each. So 5x+10y=85.

He has 10 coins altogether. So x+y=10

Now rearranging, y=10-x

Substituting that into the other equation

5x+10(10-x)=85

5x+100-10x=85

10x-5x=100-85

5x=15

x=3

y=10-3=7