Here's the solution to each problem, with a clear explanation for each:
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1) Peter has 100 dollars. His mother gives him x dollars more. How many dollars does he have now?
✔ Expression: `100 + x`
Explanation:
Peter starts with 100 dollars. He receives an additional amount represented by the variable `x`. To find his total, we simply add the two amounts together.
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2) Maria has c boxes of 10 pencils. The teacher gives her another 20 pencils. How many pencils does she have altogether?
✔ Expression: `10c + 20`
Explanation:
Each box contains 10 pencils, and she has `c` boxes, so she has `10 × c = 10c` pencils from the boxes. She gets 20 more pencils from the teacher. Total pencils = pencils from boxes + extra pencils = `10c + 20`.
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3) John bought z hamburgers at $3 each and paid with a 20 dollar note. How much change did he get?
✔ Expression: `20 - 3z`
Explanation:
Each hamburger costs $3, and he buys `z` of them, so the total cost is `3 × z = 3z` dollars. He pays with a $20 bill, so his change is the amount he paid minus the cost: `20 - 3z`.
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4) I have 200 marbles and divide them among t girls. How many marbles will each girl get?
✔ Expression: `200 ÷ t` or `200/t`
Explanation:
To divide 200 marbles equally among `t` girls, you divide the total number of marbles by the number of girls. So each girl gets `200/t` marbles.
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5) Peter is x years old. His dad is 4 times older than him. How old is his dad?
✔ Expression: `4x`
Explanation:
If Peter is `x` years old, and his dad is 4 times that age, then his dad’s age is `4 × x = 4x`.
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6) John earns x dollars per hour. Petra earns 2 dollars per hour more than him. How much do they earn altogether per hour?
✔ Expression: `x + (x + 2)` or simplified: `2x + 2`
Explanation:
John earns `x` dollars per hour. Petra earns `x + 2` dollars per hour (since she earns 2 more than John). Together, their hourly earnings are `x + (x + 2)`, which simplifies to `2x + 2`.
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7) I have 3 boxes of x paperclips. If I use 100 paperclips, how many of them will I have left?
✔ Expression: `3x - 100`
Explanation:
Each box has `x` paperclips, and there are 3 boxes, so total paperclips = `3 × x = 3x`. After using 100, the remaining amount is `3x - 100`.
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8) Indy has x erasers and y pencils. How many erasers and pencils does Indy have?
✔ Expression: `x + y`
Explanation:
Indy has `x` erasers and `y` pencils. To find the total number of items (erasers + pencils), we add them together: `x + y`.
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✔ Final Answer Summary:
1. `100 + x`
2. `10c + 20`
3. `20 - 3z`
4. `200/t`
5. `4x`
6. `2x + 2`
7. `3x - 100`
8. `x + y`
These expressions correctly translate each word problem into algebraic form using variables as numbers.
Parent Tip: Review the logic above to help your child master the concept of writing math expressions worksheet.
