Question

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?

Answer 1

To describe the situation, we can write a system of equations using variables h and m. Solving the system will give us the values for h and m, which can be added together to determine the time it takes to knit a hat and a pair of mittens.

Step-by-step explanation:

To write a system of equations, let's assign variables to the time it takes to knit a hat and a pair of mittens. Let h represent the time to knit a hat, and m represent the time to knit a pair of mittens.

From the given information, we can form two equations:

For the first fall: 4h + 3m = 56 (4 hats and 3 pairs of mittens took a total of 56 hours)

For the second fall: 3h + 1m = 27 (3 hats and 1 pair of mittens took a total of 27 hours)

Now, we can solve this system of equations using any method, such as substitution or elimination, to find the values for h and m.

Once we have the values for h and m, we can determine how long it takes Quinn to knit a hat and a pair of mittens by adding the values of h and m together.