Question

Kevin and Randy have a jar containing 52 coins all of which are either quarters and nickels the total value of the coins in the jar is $6.60 how many of each type of coin do they have

Answer 1

Answer: 32 nickels and 20 quarters :)

Step-by-step explanation:

first lets make an equation

quarters - 25 cents so 25x

nickels - 5 cents so 5y

^ in those expressions, we've established that the variable (x or y) as the amount of coins

so 25 * however many quarters plus 5 * however many nickels will give you the total amount of cents :)

since we're working in cents, lets change $6.60 to 660 cents

25x + 5y = 660

now the problem is that we cant solve this equation due to two different variables

but we know that the total amount of coins is 52, so we can state that

x + y = 52

to make this easier to eventually plug into our previous equation, just pick a variable and isolate it. i'll do x

x = 52 - y

okkk now lets plug it into our equation

25 (52 - y) + 5y = 660

1300 - 25y + 5y = 660

1300 - 20y = 660

-1300           -1300

-20y = -640

y = -640 / -20

y = 32

so we know that we have 32 nickels

now we plug in that answer to our second equation to find how many quarters

x + y = 52

x + 32 = 52

x = 52 - 32

x = 20

so we have 32 nickels and 20 quarters :))

hope this helped