You and your friend each start a car-washing service. You spend $25 on supplies and charge $10 per car. Your friend spends $55 on supplies and charges $13 per car. How many cars do you have to wash to earn the same amount of money as your friend?
y = 10x – 25
y = 13x – 55
To find out how many cars you need to wash to earn the same amount as your friend, we need to set your earnings equal to your friend’s earnings.
1. Your earnings: ( y = 10x – 25 )
2. Friend’s earnings: ( y = 13x – 55 )
Set them equal to each other:
[ 10x – 25 = 13x – 55 ]
Now, let’s solve for ( x ):
1. Subtract ( 10x ) from both sides:
[ -25 = 3x – 55 ]
2. Add 55 to both sides:
[ 30 = 3x ]
3. Divide both sides by 3:
[ x = 10 ]
So, you need to wash 10 cars to earn the same amount of money as your friend. Keep up the great work! If you need further assistance, feel free to check the extended services page.