Question

3 match each equation to a story. (two of the stories match the same equation )
a. $3(x + 5) = 17$ a. jada’s teacher fills a travel bag with 5 copies of a textbook. the weight of the bag and books is 17 pounds. the empty travel bag weighs 3 pounds. how much does each book weigh?
b. $3x + 5 = 17$ b. a piece of scenery for the school play is in the shape of a 5 - foot - long rectangle. the set designer decides to increase the length. there will be 3 identical rectangles with a total length of 17 feet. by how much did the designer increase the length of each rectangle?
c. $5(x + 3) = 17$ c. elena spends $17 on gifts for her 5 cousins. each cousin gets a book that costs $3 and the same bookmark. how much does each bookmark cost?
d. $5x + 3 = 17$ d. noah packs bags at the food pantry to deliver to families. he packs 5 bags that weigh a total of 17 pounds. each bag contains 3 pounds of groceries and a packet of papers with health - related information. how much does each packet of papers weigh?
e. andre has 3 times as many pencils as noah and 5 pens. he has 17 pens and pencils all together. how many pencils does noah have?

Explanation:

Step1: Analyze story a

Let $x$ = weight of each book. Empty bag is 3 lbs, 5 books total weight $5x$. Total weight: $5x + 3 = 17$. Matches D.

Step2: Analyze story b

Let $x$ = length increase per rectangle. Original length 5 ft, new length per rectangle $x+5$. 3 rectangles total length: $3(x+5)=17$. Matches A.

Step3: Analyze story c

Let $x$ = cost of each bookmark. Each gift: $3+x$, 5 gifts total cost: $5(x+3)=17$. Matches C.

Step4: Analyze story d

Let $x$ = weight of each paper packet. Each bag: $3+x$, 5 bags total weight: $5(x+3)=17$. Matches C.

Step5: Analyze story e

Let $x$ = Noah's pencils. Andre has $3x$ pencils +5 pens, total: $3x+5=17$. Matches B.

Answer:

• a. $\boldsymbol{D.\ 5x + 3 = 17}$
• b. $\boldsymbol{A.\ 3(x + 5) = 17}$
• c. $\boldsymbol{C.\ 5(x + 3) = 17}$
• d. $\boldsymbol{C.\ 5(x + 3) = 17}$
• e. $\boldsymbol{B.\ 3x + 5 = 17}$