Question

@Lucinda12345 Kevin and Randy have a jar containing 77 coins, which are all quarters or nickels. The total value of all the coins is $12.65 How many of each type of coin do they have?

Answer 1

You need to open it under a new question like @just_one_last_goodbye did here for you :)

Answer 2

You need to set up two equations to determine this. The first equation will represent the number of coins. Use Q to represent quarters and N to represent Nickels. So waht would the equation for the number of coins look like?

Answer 3

Oh ok @nelsonjedi will help you ^-^ while i go help the user for health science

Answer 4

ok

Answer 5

q+n=77

Answer 6

Very good. Now we need an equation to represent the total amount of the coins. How would you write that equation?

Answer 7

t stands for total?

Answer 8

Think about how much a quarter and nickel represent in value. Total would be $ 12.65.

Answer 9

so qn77=12.65?

Answer 10

Let's forget about the first equation we did. That will come in later.

Quarters equal 0.25 Nickels equal 0.05 The total of the number of nickles plus the number of quarters equals $ 12.65 So what would the equation look like?

Answer 11

what I sometimes do is guess like 30 quarters and 47 nickles and if its too much then have more nickles and less quarters. this takes forever, and i know there is an easier algebraic way that i don't know

Answer 12

i don't know much about equations

Answer 13

oh i think i know!

Answer 14

xQ+yN=77

Answer 15

If we were looking at just quarters for an equation say how many quarters are in $1.00 and quarters equal 0.25. With Q representing the number of quarters. How would you write this as an equation?

Answer 16

and 0.25x+0.5y=12.65

Answer 17

is that correct?

Answer 18

0.25 x 4 = 1.00? or is that not an equation

Answer 19

0.25x + 0.05y = 12.65
Just off a decimal place. Very good. But instead of using x and y lets use q and n.

Answer 20

ok so 0.25q + 0.05n = 12.65

Answer 21

So we would have 0.25q +0.05n = 12.65 and from our first equation we had q+n=77..Now you need to use substitution to solve.

Answer 22

so it would be
0.25q + 0.05n = 12.65
q + n = 77

Answer 23

so q = 77-n

Answer 24

Good

Answer 25

so 0.25(77-n) + 0.05n = 12.65

Answer 26

Good..go on

Answer 27

19.25 - 0.25n +0.05 n = 12.65
and then combinde like terms right?

Answer 28

19.25 - 0.20n = 12.65
-0.20n = 12.65-19.25

Answer 29

Good

Answer 30

-0.20n = -6.6

Answer 31

0.20n = 6.6

Answer 32

n = 6.6 divided by 0.20??

Answer 33

Yes

Answer 34

n = 33 so 33 nickels and 44 quarters

Answer 35

THANK YOU SO MUCH!!!!!! :)

Answer 36

Very good job..and you are welcome