amanda like to knit hats and mittens for friends and family. last fall, she knitted 2 hats and 4 pairs of mittens, which which took a total of 48 hours. this fall, she knitted 2 hats and 3 pairs of mittens, which took a total of 39 hours. if each hat and each pair of mittens takes the same amount of time to knit, how long dose it take amanda to knit a hat and a pair of mittens?

We now know that a hat takes 6 hours to knit and a pair of mittens take 9 hours to knit.

In total, it takes 15 hours to knit a hat and a pair of mittens.

Step-by-step explanation:

We can construct a system of equations to model this:

Let x represent hats and y represent mittens.

1. 2x + 4y = 48

2. 2x + 3y = 39 We can solve this system by elimination.

Mutliply equation 2, fully, by - 1 to eliminate the x's.

2x + 4y = 48

-2x - 3y = - 39 Now add the equations together.

y = 9 We can now substitute this into equation 1, or 2, to get the x value.

1. 2x + 4y = 48

2x + 4 (9) = 48

2x + 36 = 48 Subtract 36 from both sides.

2x = 12 Divide both sides by 2.

x = 6

x represented the hats, and y represented the mittens, so we now know that a hat takes 6 hours to knit and a pair of mittens take 9 hours to knit.

In total, it takes 15 hours to knit a hat and a pair of mittens.