WRITING AN EQUATION AND CHECKING SOLUTIONS 

Example 1 :

Sarah used a gift card to buy $47 worth of food. She has $18 left on her gift card. Write an equation to represent this situation and use it to determine whether Sarah had $65 or $59 on the gift card before buying food.

Solution :

Step 1 :

Write a word equation based on the situation.

Step 2 :

Rewrite the equation using a variable for the unknown quantity and the given values for the known quantities.

Let x be the amount on the card.

The amount spent and the amount left on the card are the known quantities. Substitute those values in the equation. 

Step 3 :

Substitute 65 and 59 for x to see which equation is true.

So, the amount on Sarah’s gift card before she bought food was $65.

Example 2 :

On Saturday morning, Owen earned $24. By the end of the afternoon he had earned a total of $62. Write an equation to represent the situation. Tell what the variable represents. Determine whether Owen earned $38 or $31 on Saturday afternoon.

Solution :

Step 1 :

Write a word equation based on the situation.

Amount earned on Saturday morning 

+ 

Amount earned on Saturday afternoon

||

Total money earned

Step 2 :

Let x be the amount  earned by Owen between morning and afternoon

The amount earned in the morning and total amount earned by the end of the afternoon are known quantities. Substitute those values in the equation. 

Then the word equation will become

24 + x  =  62

Step 3 :

Substitute 38 and 31 for x to see which equation is true.

So, Owen earned $38 on Saturday afternoon. 

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