Question

write 2 equations showing how many large and small glasses sold.total glasses = 29price of small glasses is .35price of large glasses is .50

Answer 1

Let's say that the number of large glases sold is L, and the number of small glasses sold is S.

We know the total number of glasses sold, considering large and small ones is 29. Then:

`L+S=29`

The sales of the large glasses could be calculated as the number of large glasses sold times the price of each:

`\text{0}.50\cdot L`

The same for the small glasses:

`\text{0}.35\cdot S`

Then, the total sales, which are 13.45, will be the sum of the sales of small glasses and the sales of the small ones. Then:

`0.5\cdot L+0.35\cdot S=13.45`

Then, we have a system of 2 equations to calculate the number of small glasses and large glasses:

`\begin{gathered} L+S=29 \\ 0.5L+0.35S=13.45 \end{gathered}`

With the first equation we can say:

`L=29-S`

Replacing this expression for L in the second equation of the system we have:

`0.5(29-S)+0.35S=13.45`

Solving for S:

`\begin{gathered} 0.5\cdot29-0.5S+0.35S=13.45 \\ 14.5-0.15S=13.45 \\ -0.15S=13.45-14.5 \\ S=(-1.05)/(-0.15) \\ S=7 \end{gathered}`

The number of small glasses sold is 7. Then, recalling that L = 29 - S:

`\begin{gathered} L=29-7 \\ L=22 \end{gathered}`

The number of large glasses sold is 22.