QuestionAnn spends \$89 on software and \$394 on ads. Each art costs \$14 to make and sells for \$35. How many must she sell?

Studdy Solution

STEP 1

Assumptions1. The cost of software is \$89. The cost of online advertisements is \$3943. The cost of printing and framing each piece of art is \$144. The selling price of each piece of art is \$355. Ann needs to sell enough pieces of art such that her sales equal her expenses

STEP 2

First, we need to find the total cost of Ann's expenses. This includes the cost of software, online advertisements, and the cost of printing and framing each piece of art.
$Expenses = Software\, cost + Advertisement\, cost + (Printing\, and\, framing\, cost \times Number\, of\, pieces)$

STEP 3

Now, we need to find the total sales. This is the selling price of each piece of art multiplied by the number of pieces sold.
$Sales = Selling\, price \times Number\, of\, pieces$

STEP 4

For Ann's sales to equal her expenses, we set the two equations equal to each other and solve for $a$ , the number of pieces of art.
$Sales = Expenses$ $elling\, price \times Number\, of\, pieces = Software\, cost + Advertisement\, cost + (Printing\, and\, framing\, cost \times Number\, of\, pieces)$

STEP 5

Substitute the given values into the equation.
$35a =89 +394 +14a$

STEP 6

implify the equation by subtracting $14a$ from both sides.
$35a -14a =89 +394$

STEP 7

This simplifies to $21a =483$

STEP 8

Finally, solve for $a$ by dividing both sides of the equation by21.
$a =483 /21$

STEP 9

Calculate the value of $a$ .
$a =23$ Ann needs to sell23 pieces of art for her sales to equal her expenses.

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