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y : total number of math pr
Step 2a: Write an equation problems that Mr. Taylor w

y=3x+6
Step 2b: Write an equation to problems that Mrs. Pippin wil

y=5x+2

$y$ : total number of math pr $\newline$ Step $2$ a: Write an equation problems that Mr. Taylor w $\newline$ $y=3 x+6$ $\newline$ Step $2$ b: Write an equation to problems that Mrs. Pippin wil $\newline$ $y=5 x+2$

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Evaluate a linear function: word problems

Full solution

Q.

y

: total number of math pr

\newline

Step

2

a: Write an equation problems that Mr. Taylor w

\newline

y=3 x+6

\newline

Step

2

b: Write an equation to problems that Mrs. Pippin wil

\newline

y=5 x+2

Set Equations Equal: Set the two equations equal to each other because Mr. Taylor and Mrs. Pippin will write the same number of problems. $\newline$ So, we have $3x + 6 = 5x + 2$ .
Subtract $x$ Terms: Subtract $3x$ from both sides to get the $x$ terms on one side. $\newline$ This gives us $6 = 2x + 2$ .
Isolate $x$ Term: Subtract $2$ from both sides to isolate the term with $x$ . $\newline$ So, we get $4 = 2x$ .
Divide to Solve: Divide both sides by $2$ to solve for $x$ . $\newline$ This gives us $x = 2$ .
Substitute x Value: Substitute $x = 2$ back into either original equation to find the total number of problems $y$ . Let's use Mr. Taylor's equation: $y = 3(2) + 6$ .
Multiply and Add: Multiply $3$ by $2$ and then add $6$ . $\newline$ So, $y = 6 + 6$ .
Find Total Problems: Add $6$ and $6$ to get the total number of problems. $\newline$ So, $y = 12$ .

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