Zoe is making greeting cards, which she will sell by the box at an arts fair. She paid $48 for a booth at the fair, and the mate

Question

3 years ago

7

Zoe is making greeting cards, which she will sell by the box at an arts fair. She paid $48 for a booth at the fair, and the mate

rials for each box of cards cost $6. She will sell the cards for $10 per box of cards. At some point, she will sell enough cards so that her sales cover her expenditures. How much will the sales and expenditures be? How many cards will that take?

Mathematics

1 answer:

klasskru [66] · Answer 1 · 2021-11-28T08:03:23+03:00

The sales and expenditures will be $120 and it will take 12 card boxes.

Step-by-step explanation:

Cost of booth = $48

Expenditure per card box = $6

Let,

x be the number of card boxes.

Total cost as a function of x.

T(x)= 48+6x Eqn 1

Selling price of one card box = $10

Total sales as a function of x, where x is the no. of card boxes

S(x) = 10x Eqn 2

For expenditures and sales to be same

T(x) = S(x)

$48+6x=10x\\48=10x-6x\\48=4x\\4x=48$

Dividing both sides by 4

$\frac{4x}{4}=\frac{48}{4}\\x=12$

Putting x=12 in both Equations

$T(12)=48+6(12)\\T(12)=48+72\\T(12)=\$120$

$S(12)=10(12)\\S(12)=\$120$

The sales and expenditures will be $120 and it will take 12 card boxes.

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