Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Quinn likes to knit hats and mittens for friends and family. Last fall, she knitted 4 hats and 3 pairs of mittens, which took a total of 56 hours. This fall, she knitted 3 hats and 1 pair of mittens, which took a total of 27 hours. If each hat and each pair of mittens takes the same amount of time to knit, how long does it take Quinn to knit a hat and a pair of mittens?

hats = 5

mittens = 12

Step-by-step explanation:

hats = h

mittens = m

Uknown:

- How many hours per hats

- How many hours per mittens

Known:

- How many hours in total

- How many pairs of mittens made

- How many pairs of hats made

4h + 3m = 56

3h + 1m = 27

3h + m = 27

m = -3h + 27

4h + 3m = 56

4h + 3(-3h + 27) = 56

4h - 9h + 81 = 56

-5h = 56 - 81

-5h = -25

-5h/5 = -25/5

-h = -5

-h/-1 = -5/-1

h = 5

3h + m = 27

3(5) + m = 27

15 + m = 27

m = 27 - 15

m = 12

Check: h = 5, m = 12

4h + 3m = 56

3h + 1m = 27

4h + 3m = 56

4(5) + 3(12) = 56

20 + 36 = 56

56 = 56

3h + 1m = 27

3(5) + (12) = 27

15 + 12 = 27

27 = 27

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

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step-by-step explanation: