Let's solve each of these algebra word problems by writing an equation for each situation. We'll go step by step and explain the reasoning.
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1. Jerry had 20 DVDs. He bought x more. Then he had 28 DVDs.
- Jerry started with 20 DVDs.
- He bought
x more, so total becomes: $ 20 + x $
- After buying, he has 28 DVDs.
So the equation is:
$$
20 + x = 28
$$
✔ Answer: $ 20 + x = 28 $
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2. Dorothy baked 4 loaves of banana bread, each weighs w oz. The total weight is 80 oz.
- Each loaf weighs $ w $ ounces.
- There are 4 loaves, so total weight = $ 4 \times w = 4w $
- Total weight is 80 oz.
So the equation is:
$$
4w = 80
$$
✔ Answer: $ 4w = 80 $
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3. Bobbie had z tokens. She gave 7 to Bryan. She had 16 tokens left.
- Bobbie originally had $ z $ tokens.
- She gave away 7, so she has $ z - 7 $ left.
- She has 16 left.
So the equation is:
$$
z - 7 = 16
$$
✔ Answer: $ z - 7 = 16 $
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4. Each of the 50 states has s U.S. Senators. There are 100 U.S. Senators all together.
- Each state has $ s $ senators.
- There are 50 states.
- Total number of senators = $ 50 \times s = 50s $
- Total is 100.
So the equation is:
$$
50s = 100
$$
✔ Answer: $ 50s = 100 $
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5. The recess period at Morehead School is usually 20 minutes. On Friday, the students are given an extra t minutes, so they had 40 minutes for recess.
- Usual recess = 20 minutes.
- Extra time = $ t $ minutes.
- Total recess on Friday = $ 20 + t $
- This equals 40 minutes.
So the equation is:
$$
20 + t = 40
$$
✔ Answer: $ 20 + t = 40 $
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6. Deborah dealt an entire deck of 52 cards to make g hands. Each hand had 13 cards.
- Total cards = 52.
- Each hand has 13 cards.
- Number of hands = $ g $
- So total cards = $ 13 \times g = 13g $
- This equals 52.
So the equation is:
$$
13g = 52
$$
✔ Answer: $ 13g = 52 $
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✔ Final Answers:
1. $ 20 + x = 28 $
2. $ 4w = 80 $
3. $ z - 7 = 16 $
4. $ 50s = 100 $
5. $ 20 + t = 40 $
6. $ 13g = 52 $
These equations represent each situation algebraically. You can solve them if needed, but the task only asks to write the equations.
Parent Tip: Review the logic above to help your child master the concept of writing algebraic equations from word problems worksheet.
