Answer:
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.
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