John is making 3 1/2 batches of cookies. Each batch takes 2 1/4 cups of flour. How much flour will John need for the cookies?
1 answer:
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If and
, then you can replace
in either equation with the equivalent expression given by the other equation. In this case, you have
and you can solve for .
Then .
For the second system, you can write
Then substitute this into the second equation and you get
so that
We have the equation for company 1: y = 3x + 5. That means it costs $3 to rent a movie with a $5 fee no matter how many movies you rent. It would benefit us to have the equation for company 2, so we need to find it using 2 points on the line. I picked the points (2,14) and (0,12). Find the slope of this by using the slope formula: 
which gives us a slope of 1. Now we can use that slope and the slope-intercept form of a line to find the y-intercept, which serves as the fee for renting from company 2. 14=1(2)+b and 14 = 2 + b and b = 12. The equation then for company 2 is y=1x+12. This means it costs $1 to rent movies, but your fee to rent, no matter how many movies you pick, is $12. The "rate of change" in the choices refers to the slope. The slope in company 1's equation is 3 and the slope in company 2's equation is 1. The best description is the first choice that says "There is a higher rate of change at Company 1".