Question

tammy and lia work in retail, in different shops. Tammy makes $7 per hour plus $4 for each item she sella, and Lie makes $10 per hour plus $3 for every item she sells. In an hour, how many items do they need to sell to make the same amount of money

Answer 1

So lets say y = The amount of money that's made and x = The number of hours worked. We need two equations. one for Tammy and one for Lia. Tammy's equation will be: y=7x+4 because she makes 7 dollars an hour plus 4 dollars for every item she sells. Lia's equation should be: y=10x+3 because she makes 10 dollars an hour plus 3 dollars for every item she sells. Now since we need to know when they will make the same amount of money, we put both the equations together to make 7x+4=10x+3. Now lets use the distributive property to solve that equation.

7x+4=10x+3

    -4         -4

      7x=10x-1

    -10x -10x

-3x=-1

x=0.3 repeated)

Now we plug x into Lia's equation and solve that.

y=10($\frac{1}{3}$)+3

y=3.33+3

y=6.33

Now we write our answer as an ordered pair: (0.33, 6.33)

Buuuuuuuuuuuttt you can't have 0.333333333333 of an item so the final answer here would be NO SOLUTION.