Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ Leah and her sister Carly are making baby blankets to sell at a boutique. Leah has already completed $2$ blankets and can finish $5$ more blankets per day. Carly has already completed $12$ blankets and can finish $4$ more blankets per day. At some point, they will have completed the same number of blankets. How long will that take? How many blankets will each woman have made? $\newline$ After $\_$ days, each woman will have finished $\_$ blankets.

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Solve a system of equations using substitution: word problems

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

\newline

Leah and her sister Carly are making baby blankets to sell at a boutique. Leah has already completed

2

blankets and can finish

5

more blankets per day. Carly has already completed

12

blankets and can finish

4

more blankets per day. At some point, they will have completed the same number of blankets. How long will that take? How many blankets will each woman have made?

\newline

After

\_

days, each woman will have finished

\_

blankets.

Define Variables: Let's define the variables for the number of days it will take for Leah and Carly to have completed the same number of blankets as $x$ . Let's also define the total number of blankets Leah will have made as $L$ and the total number of blankets Carly will have made as $C$ . We can write two equations to represent the situation: $\newline$ For Leah: $L = 2 + 5x$ (since she has already completed $2$ blankets and can finish $5$ more per day) $\newline$ For Carly: $C = 12 + 4x$ (since she has already completed $12$ blankets and can finish $4$ more per day) $\newline$ We want to find the value of $x$ when $L$ equals $C$ .
Set Equations Equal: Now we set the two equations equal to each other because we are looking for the point at which Leah and Carly will have completed the same number of blankets: $\newline$ $2 + 5x = 12 + 4x$ $\newline$ This is the equation we will solve to find the number of days it will take for them to have the same number of completed blankets.
Solve for x: To solve for x, we will subtract $4x$ from both sides of the equation to get the x terms on one side: $\newline$ $2 + 5x - 4x = 12 + 4x - 4x$ $\newline$ This simplifies to: $\newline$ $2 + x = 12$
Determine Blankets After $10$ Days: Next, we subtract $2$ from both sides of the equation to isolate $x$ : $\newline$ $2 + x - 2 = 12 - 2$ $\newline$ This simplifies to: $\newline$ $x = 10$ $\newline$ So, it will take $10$ days for Leah and Carly to have completed the same number of blankets.
Determine Blankets After $10$ Days: Next, we subtract $2$ from both sides of the equation to isolate $x$ : $\newline$ $2 + x - 2 = 12 - 2$ $\newline$ This simplifies to: $\newline$ $x = 10$ $\newline$ So, it will take $10$ days for Leah and Carly to have completed the same number of blankets.Now we need to determine how many blankets each woman will have made after $10$ days. We can substitute $x = 10$ into the original equations for $L$ and $C$ . $\newline$ For Leah: $L = 2 + 5(10) = 2 + 50 = 52$ $\newline$ For Carly: $x$ $0$ $\newline$ Therefore, after $10$ days, each woman will have finished $x$ $2$ blankets.