Lesson 6
Distinguishing between Two Types of Situations
Let’s think about equations with and without parentheses and the kinds of situations they describe.
Problem 1
A school ordered 3 large boxes of board markers. After giving 15 markers to each of 3 teachers, there were 90 markers left. The diagram represents the situation. How many markers were originally in each box?
![Tape diagram. Three equal parts labeled, x minus 15, total 90.](https://cms-im.s3.amazonaws.com/oF3RvCuTnVj7nABLCD8XJVEn?response-content-disposition=inline%3B%20filename%3D%227-7.6.A2.newPP.02.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.A2.newPP.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233753Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ad767e53b484c1988fef90eb27f70150782792a3193cebed1faf6348da271701)
Problem 2
The diagram can be represented by the equation \(25=2+6x\). Explain where you can see the 6 in the diagram.
![Tape diagram, 1 part labeled 2, 6 parts labeled x, total 25.](https://cms-im.s3.amazonaws.com/vtywVMeNe7FWYWsqakDDF44e?response-content-disposition=inline%3B%20filename%3D%227-7.6.A3.newPP.06.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.A3.newPP.06.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233753Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0c749fd38a701bac8def84fe8ae7988f42ee1087e6d45f2cb08de98aa11386ec)
Problem 3
Match each equation to a story. (Two of the stories match the same equation.)
- \(3(x+5)=17\)
- \(3x+5=17\)
- \(5(x+3)=17\)
- \(5x+3=17\)
- 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?
- A piece of scenery for the school play is in the shape of a 5-foot-long rectangle. The 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?
- Elena spends $17 and buys a $3 book and a bookmark for each of her 5 cousins. How much does each bookmark cost?
- Noah packs up 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?
- 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?
Problem 4
Elena walked 20 minutes more than Lin. Jada walked twice as long as Elena. Jada walked for 90 minutes. The equation \(2(x+20)=90\) describes this situation. Match each expression with the statement in the story with the expression it represents.