Graphing Systems of Equations

Jada told Noah that she has $2 worth of quarters and dimes in her pocket and 17 coins all together. She asked him to guess how many of each type of coins she had.

Let's explore some combinations of quarters and dimes that equal $2. Here is a table that shows some combinations of quarters and dimes that are worth $2. Complete the table. Write the table on a sheet of paper, you will need it later to graph.

Now let's explore some combinations of quarters and dimes that are a total of 17 coins. Here is a graph of the relationship between the number of quarters and the number of dimes when there are a total of 17 coins. What does point A represent?

Tags

CCSS.8.EE.B.5

How much money, in dollars, is the combination represent by point A worth?

Tags

CCSS.5.G.A.2

Is it possible for Jada to have 4 quarters and 13 dimes in her pocket? Explain how you know. Remember Jada told Noah she had $2 worth of quarters and dimes in her pocket and 17 coins all together.

Tags

CCSS.4.MD.A.2

Plot all the ordered pairs in the table from problem number 1 on the graph provided. You should have written it down on a sheet of paper to use later,

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

What did you notice about the points you plotted?

Tags

CCSS.5.G.A.2

How many quarters and dimes must Jada have in her pocket? How is this solution related to the graph? Explain how you know.

Tags

CCSS.8.EE.C.8C

Claire and Alison are making signs for all the lockers as part of the decorations for the upcoming spirit week. Yesterday, Alison made 15 signs and Claire made 5 signs. Today, they need to make more signs. Each person's progress today is shown in the coordinate plane. Which line represents Claire's progress? ​ (a)  

Which line represents Alison's progress? ​ (b)  

• Blue line
• Black line