Math Problem Statement
If 8 pens and 4 rulers cost $116 and 2 pens and 6 rulers cost$54. Find the cost of 30 pens and 30 rulers. Give simple step by step explanation for Grade 3 students.
Solution
Let’s solve this together, step by step.
Step 1: Write down what we know.
We have two pieces of information:
- 8 pens + 4 rulers = $116
- 2 pens + 6 rulers = $54
Let’s say:
- Each pen costs P dollars.
- Each ruler costs R dollars.
So, we can write the information as two math sentences (equations):
- 8P + 4R = 116
- 2P + 6R = 54
Step 2: Make the math simpler.
Let’s make these equations easier to work with.
-
8P + 4R = 116 — We can divide everything here by 4:
- This becomes 2P + R = 29
-
So now we have two simpler equations:
- 2P + R = 29
- 2P + 6R = 54
Step 3: Subtract to find R (cost of a ruler).
Now we can subtract the first equation from the second one to get R.
- (2P + 6R) - (2P + R) = 54 - 29
- This simplifies to 5R = 25
- Divide by 5: R = 5
So, each ruler costs $5.
Step 4: Find P (cost of a pen).
Now we can use R = 5 in the first equation to find P.
- 2P + R = 29
- Substitute R = 5:
- 2P + 5 = 29
- Subtract 5 from both sides: 2P = 24
- Divide by 2: P = 12
So, each pen costs $12.
Step 5: Find the cost of 30 pens and 30 rulers.
Now, we know:
- Each pen costs $12.
- Each ruler costs $5.
To find the cost of 30 pens and 30 rulers:
- Cost of 30 pens = 30 x 12 = $360
- Cost of 30 rulers = 30 x 5 = $150
Add them together:
- Total cost = $360 + $150 = $510
Final Answer:
The cost of 30 pens and 30 rulers is $510.
Would you like more details or have any questions?
Practice Questions
- If 10 pens and 5 rulers cost $X, how much is X?
- How much would 5 pens and 2 rulers cost?
- What if the cost of 3 pens and 7 rulers was needed?
- Can you find the cost of 15 pens and 20 rulers?
- How much would it be to buy 50 pens only?
Tip: When you have two equations, try simplifying them to make solving easier!
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Math Problem Analysis
Mathematical Concepts
Basic Algebra
Systems of Equations
Multiplication and Addition
Formulas
Cost calculation: Total cost = (quantity of item 1 × cost of item 1) + (quantity of item 2 × cost of item 2)
Theorems
Substitution method in algebra
Suitable Grade Level
Grades 3-5
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