One week a store sold 45 pens.

Question

One kind sold for $8.50 and another for $9.75. If $398.75 was taken in, how many of each kind were sold?

Answer 1

We are gonna start by saying that $8.50 is x, and $9.75 is y, and the total of pens equals 45.

Then, combine everything together to make the equation of x+y=45

Remember that $398.75 is the total money taken in, making the second equation 8.50x + 9.75y= 398.75

We'll start by solving for x, so make it so it's by itself on one side,

x + y= 45 --> subtract y to the other side making it x = 45 - y

Now that we know what "x" is, use the second equation we found to substitute the "x" for (45-y)

8.50x + 9.75y= 398.75 ---> 8.50(45-y) + 9.75y= 398.75

Now, multiply both 8.50 times 45 and 8.50 times y, and plug it back into the equation,

382.50 - 8.50y + 9.75y= 398.75

Subtract 382.50 from both sides making the y be by itself, and add like terms,

-8.50y + 9.75y = 398.75 - 382.50 --> 1.25y= 16.25

Divide both sides by 1.25,

1.25y /1.25 = 16.25 / 1.25

y= 13

Now that we have y, substitute it into the first equation x= 45 - y

x = 45 - 13

x= 32

You can check you answer by multiplying 8.50 times 32= 272 and 9.75 times 13= 126.75, and add them together to get 398.75

Answer 2

x = number of pen type x sold

y = number of pen type y sold

x + y = 45

money taken in for pen type x = 8.50x

money taken in for pen type y = 9.75y

total money taken in 398.75

8.50x + 9.75y = 398.75

two equations in two unknowns, which you can go ahead and solve. please contact me if you have further questions.