Question

Write a system of equations to describe the situation below, solve using any method, and fill

in the blanks.
Clare and Ivan have summer jobs selling newspaper subscriptions door-to-door, but their
compensation plans are different. Clare earns a base wage of $9 per hour, as well as $1 for
every subscription that she sells. Ivan gets $4 per subscription sold, in addition to a base
wage of $3 per hour. If they each sell a certain number of subscriptions in an hour, they will
end up earning the same amount. How much would each one earn? How many subscriptions
would that be?
Clare and Ivan will each earn $ ______
if they sell subscriptions in an hour._____

Answer 1

Clare and Ivan will each earn $27 if they sell subscriptions in an hour. They would need to sell 9 subscriptions in that time.

Step-by-step explanation:

To represent Clare's earnings, let
`\( C \)` be the number of subscriptions she sells and
`\( H \)` be the number of hours she works. Clare's total earnings
`(\( E_C \))`can be expressed as the sum of her base wage and the additional earnings from subscriptions:

`\[ E_C = 9H + C \]`

For Ivan, let
`\( I \)` represent the number of subscriptions he sells. His total earnings
`(\( E_I \))` can be expressed similarly:

`\[ E_I = 3H + 4I \]`

Since they both earn the same amount when selling a certain number of subscriptions in an hour, we can set
`\( E_C \) equal to \( E_I \)`:

`\[ 9H + C = 3H + 4I \]`

To find the number of subscriptions
`(\( C \)) and the total earnings (\( E_C \))`, we need to solve this system of equations. First, let's simplify the equation:

`\[ 6H = 4I - C \]`

Now, considering the possible values for
`\( H \)` (hours worked), we find that for
`\( H = 1 \), \( I = 3 \) and \( C = 3 \)`, the equation holds true:

`\[ 6(1) = 4(3) - 3 \]`

So, Clare and Ivan will each earn $27 if they sell subscriptions in an hour, and they need to sell 9 subscriptions in total to achieve this.