Charlotte’s weekly paycheck is based on the number of hours worked during the week and on the weekend. if she works 13 hours during the week and 14 hours on the weekend, she earns $250.90. if she works 15 hours during the week and 8 hours on the weekend, she earns $204.70. how much more does charlotte earn per hour on the weekends than she earns during the week? round to the nearest cent.

Let's say that x is the number of dollars she makes per hour during the week and y is the number of dollars she makes per hour on the weekend. We have 2 equations we can write given the info we have. The equations are the number of hours during the week plus the number of hours on the weekend equals a specific amount of money. That general equation is what we will use for both equations. 13x + 14y = 250.90 and 15x + 8y = 204.70. We need to solve for both x and y. But we can't have 2 unknowns so we need to eliminate one. I am going to multiply the first equation by -8 and the second equation by 14 which will effectively eliminate the y's. Doing that multiplication gives us 2 new equations that are -104x - 112y = -2007.20 and 210x +112y = 2865.80. As you can see, the y terms cancel out, leaving us with this single equation in terms of x only: 106x = 858.60. If we divide both sides by 106 we find that the amount she makes per hour during the week is $8.10. Now we will use that value for x and sub it into one of the original equations to solve for y. 13(8.10) + 14y = 250.90 and 105.30 + 14y = 250.90. We subtract 105.30 from both sides giving us 14y = 145.60 and divide to get y = 10.40. That means that she makes $10.40 per hour on the weekends. In the end, when she works on the weekends, she makes $2.30 more per hours.

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