Math problem

Question

Kevin and Randy Muise have a jar containing 57 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $ 7.05
How many of each type of coin do they have?

Answer 1

Ok, so you know they have 57 coins, nickels and quarters... make an equation => n (nickels) + q (quarters) = 57.

 

then, we know the value of each and how much they have total, so make another equation=> 

(.05*n) + (.25*q) = 7.05

 

now you have a system of equations, so solve that!

n+q=57

.05n +.25q= 7.05

 

solve for n:

n = 57-q

then:

.05(57-q) +.25q= 7.05

 

2.85 - .05q + .25q = 7.05

 

.20q = 4.20

q= 21

 

Now solve for n!

n + (21) = 57

n = 36

 

And check It!

.05(36) + .25(21) = 7.05!

 

😊😊😊

 

Answer 2

Let's say they have x quarters and (57 - x) nickels

 

0.25x + .05(57 - x) = 7.05

 

Multiply both sides of the equation by 100 to clear the decimals

 

25x + 5(57 - x) = 705

 

25x + 285 - 5x = 705

 

20x + 285 = 705

 

20x = 420

 

x = 21

 

They have 21 quarters and 57 - 21 = 36 nickels