Carlos needs 24 inches of fabric for a pillow that he is making. The fabric store has a piece of material 3/4 of a yard long that is already cut that he can buy for $5.50. If he has the exact size piece he needs cut from a bolt of fabric, it will cost $8.98 a yard. a.) Is the piece of material that is already cut large enough for his pillow? b.) What would be the cost of having exactly 24 inches of fabric cut? c.) Which is the better buy for Carlos?

a. the piece is already large enough

b. about $5.9866666666 or round to $5.99 for exactly 24 inch

c. The first option is a better buy

Step-by-step explanation:

a. convert 3/4 yard to inches. 1 yard = 36 inch. so 0.75yd / x = 1 / 36

solve and get x = 27 inches, this is more than 24 inches needed.

b. first find how many yards you need, that is same as 24 inch.

1 / 36 = x / 24 inch

x = 2/3 yards

next find how much price would be:

8.98 / 1 = x / 2/3

x = 8.98(2/3) = about $5.99

c. compare the two prices, $5.50 is less than $5.99 so the first option is better.

I spent a while to explain - please rate/like, thank you!

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3