Question

Eric and Nancy both had a successful year selling fish tanks for theirrespective employers, and so they were both given raises.Eric: Eric's base salary is still $1400, but now he makes a commission of$100 for each fish tank that he sells.Nancy: Nancy now gets a base salary of $500 per month, but her commissionhas stayed the same at $250 per fish tank.Eric and Nancy still want to make sure that they contribute the same amountto their total monthly income, and Nancy proposes using algebra to figureout how many fish tanks that they would each need to sell. She tells Ericthat he can calculate his monthly income by using the formula f(x) = 100x +1400. She says that she can calculate her own salary by using the functiong(x) = 250x + 500.1.How many fish tanks would each person need to sell so that they made the same amount of money

Answer 1

For this question, since we need to show that Eric and Nancy contributes the same amount to their monthly income, we just need to equate both expressions with each other, and then solve for the value of x.

`f(x)=g(x)`
`100x+1400=250x+500`
`100x-250x=500-1400`
`-150x=-900`
`(-150x)/(-150)=(-900)/(-150)`
`x=6`

In order to check if we got the right answer, we just need to substitute the value of x to both equations.

`100x+1400=250x+500`
`100(6)+1400=250(6)+500`
`600+1400=1500+500`
`2000=2000`

Therefore, we can conclude that Eric and Nancy has to sell 6 fish tanks each.