112 ceramics sold for $448
288 plastics sold for $1008
Use the process of elimination, so
which will equate to
For the last bit, multiply the number of plastic cups by their price, and do the same with the ceramic cups to find out the dollar value of each type of cup sold.
288 plastic cups and 112 ceramic cups.
$1008 for plastic cups and $448 for ceramic cups.
To solve this problem we will have to lay some ground work. First, we identify the variables.
Let x = the number of plastic cups sold
Let y = the number of ceramic cups sold
Now we need 2 equations using these variables.
Because we know that there were 400 total cups sold, we know that
x + y = 400
We also know that the total cost of both types of cups is $1456. Because each plastic cup costs $3.50 and each ceramic cup costs $4.00, we can say that
3.5x + 4y = 1456
Now that we have these things, we can start solving.
Subtract y from both sides of the first equation to solve for x.
x = 400 - y
Substitute this for x in the second equation.
3.5 ( 400 - y ) + 4y = 1456
1400 - 3.5y + 4y = 1456
Combine like terms and subtract 1400 from both sides.
0.5y = 56
Multiply both sides by 2
y = 112
Now that you have the number of ceramic cups, you can subtract it from 400 via the first equation to find that the number of plastic cups is 288.
These numbers can be used in turn to find the revenue generated by each type of cup.
$3.50 multiplied by 288 is $1008.
$4.00 multiplied by 112 is $448.
I do hope you have found this to be helpful. Let me know if you need more or if I was mistaken somehow.
The store sold
The price of the cups was
Dollar value of
Dollar value of
Total dollar value of
And because that addition equalized, then we know the answers above to both quantity sold and dollar value are correct.