Question

story jaylin buys 3 bags of bagels. the store gives her 5 bagels for free, making it 32 bagels total. equation $3x + 5 = 32$ tape diagram diagram with three x segments and one 5 segment, total 32 synthesis here is a new situation. explain how the number 5 is important in each representation. in the story... in the equation... in the tape diagram...

Explanation:

Step1: Solve for x in the equation

First, isolate the term with x by subtracting 5 from both sides of the equation:
$$3x + 5 - 5 = 32 - 5$$
$$3x = 27$$
Then divide both sides by 3:
$$\frac{3x}{3} = \frac{27}{3}$$
$$x = 9$$

Step2: Connect x=9 to the story

The variable $x$ represents the number of bagels in each of the 3 bags Jaylin bought. Since $x=9$, each bag has 9 bagels.

Step3: Connect x=9 to the tape diagram

The three blue $x$ sections in the tape diagram each represent the number of bagels in one purchased bag, so each $x$ equals 9.

Answer:

• In the story: The number 9 is the number of bagels in each of the 3 bags Jaylin bought. 3 bags of 9 bagels plus 5 free bagels gives $3(9)+5=32$ total bagels, which matches the story.
• In the equation: The number 9 is the solution for $x$, where $3x+5=32$ simplifies to $x=9$.
• In the tape diagram: The number 9 is the value of each of the three $x$ segments, which represent the bagels in each purchased bag. Adding these three segments ($9+9+9$) plus the 5 free bagels equals the total 32 bagels shown.