# Lesson 8 Shopping for Cats and Dogs Develop Understanding

## Learning Focus

Develop intuitive strategies for solving systems of linear equations in standard form.

How can I use logical reasoning to solve for two unknown values when I am given two pieces of information about those values?

## Open Up the Math: Launch, Explore, Discuss

Clarita is upset with Carlos because he has been buying cat and dog food without recording the price of each type of food in their accounting records. Instead, Carlos has just recorded the total price of each purchase, even though the total cost includes more than one type of food. Carlos is now trying to figure out the price of each type of food by reviewing some recent purchases.

As Carlos is examining the first set of purchases, he realizes that he can figure out the cost of the individual items just by reasoning about the numbers and the assumption that the price of each item remained the same for each shopping trip. Clarita is surprised that Carlos can find the individual prices without using tables, graphs, or equations.

See if you can reason about these shopping scenarios as well as Carlos by figuring out the cost of each item purchased without using tables, graphs, or equations.

### 1.

One week Carlos bought *Tabitha Tidbits* and *Figaro Flakes* for *Tabitha Tidbits* and * Figaro Flakes* for

### 2.

One week Carlos bought *Brutus Bites* and *Milo Munchies* for *Brutus Bites* and *Milo Munchies* for

### 3.

Carlos purchased

Pause and Reflect

### 4.

One week Carlos purchased

### 5.

Carlos has noticed that because each of his purchases have been somewhat similar, it has been easy to figure out the cost of each item. However, his last set of receipts has him puzzled. One week he tried out cheaper brands of cat and dog food. On Monday he purchased

## Ready for More?

One week Carlos bought

## Takeaways

Summarize the strategies you used to reason about the price of individual items in the context of purchasing different combinations of those items. What are some key ideas that seem helpful?

## Lesson Summary

In this lesson, we developed a strategy for finding the price of individual items from knowing the total cost of purchasing different combinations of those items. We realized we could invent purchases that weren’t actually made by doubling or tripling a known purchase or adding two purchases together. Finding two purchases in which the number of one of the items purchased was the same gave us insights into how to find the price of each individual item.

### 1.

Solve the system of equations graphically, and then state the solution.

Solution:

### 2.

Write an inequality to represent this context. Then list at least five solutions that fit the context.

Context: Fernando plans to donate at least

#### a.

Inequality

#### b.

Possible solutions