Question 252396
What we have here is the classic money problem. You will set up two equations with two unknowns. The first equation I call the "value" equation. It deals with the money. Don't use decimals or dollar signs.The second equation I call the "number" equation. It tells you total number of items. So, here they are:
{{{3.5P + 4C = 1458}}}
{{{P + C = 400}}}
here I use P = plastic and C = ceramic.
step #1 - multiply the second equation by -4.
{{{3.5P + 4C =  1458}}}
{{{-4P -  4C = -1600}}}
step #2 - You can see by adding down, we eliminate the C values.
{{{-0.5P = -144}}}
step #3 - Solving for P. we get P = 288. We can easily see that C = 112.
Now the total amount spent on plastic cups was 3.5(288) = $1,008, and the total amount spent on ceramic cups was 112(4) = $448.