Math Problem Statement

Applying the strategies of problem solving, answer the following and show your solution for each math problem.

Solution

Let's solve each question step-by-step.


  1. Olive Oil Cost at the Supermarket:

    • Grocery store price for a bottle: 7 euros.
    • Supermarket price: 7 euros + 2 euros = 9 euros per bottle.
    • Total cost for 7 bottles: 7×9=637 \times 9 = 63 euros.
  2. Cost of Pen and Pencil:

    • Let the cost of the pencil be xx.
    • Then, the cost of the pen is x+5x + 5.
    • The total cost is x+(x+5)=5.10x + (x + 5) = 5.10.
    • Solving 2x+5=5.102x + 5 = 5.10: 2x=0.10    x=0.052x = 0.10 \implies x = 0.05
    • Pencil costs 0.050.05 euros, and the pen costs 0.05+5=5.050.05 + 5 = 5.05 euros.
  3. Sum of Whole Numbers from 1 to 200:

    • Use the formula for the sum of an arithmetic series: S=n2×(a+l)S = \frac{n}{2} \times (a + l) where n=200n = 200, a=1a = 1, and l=200l = 200.
    • S=2002×(1+200)=100×201=20100S = \frac{200}{2} \times (1 + 200) = 100 \times 201 = 20100.
  4. Area of a Rectangular Garden:

    • Length =12= 12 m, Width =5= 5 m.
    • Area =12×5=60= 12 \times 5 = 60 square meters.
  5. Games Played by Joe:

    • Let the number of games Joe played be xx.
    • Kyra played x+4x + 4, and together they played 12 games.
    • Equation: x+(x+4)=12x + (x + 4) = 12.
    • Solving 2x+4=122x + 4 = 12: 2x=8    x=42x = 8 \implies x = 4
    • Joe played 4 games.
  6. Original Price of the Shirt:

    • Sale price is 1818, which is half of the original price.
    • Original price =18×2=36= 18 \times 2 = 36 dollars.
  7. Age of Aunt Amber:

    • Clues:
      1. Age is between 19 and 30.
      2. Age is a multiple of 3.
      3. Age is an even number.
    • Possible even multiples of 3 between 19 and 30 are 24 and 30.
    • Age of Aunt Amber is 24.
  8. Miles Equivalent for 11.27 Kilometers:

    • Given that 8 km = 4.83 miles, we find the conversion factor: 4.838=0.60375 miles per km\frac{4.83}{8} = 0.60375 \text{ miles per km}
    • For 11.27 km: 11.27×0.60375=6.8 miles (approximately)11.27 \times 0.60375 = 6.8 \text{ miles (approximately)}

Would you like any further explanations or have any questions?


Here are some related questions:

  1. How would the total cost change in Question 1 if each bottle of olive oil increased by 3 euros instead of 2?
  2. What would be the cost of 3 pens and 2 pencils based on Question 2?
  3. Can you find the sum of all even numbers from 1 to 200?
  4. If Kyra and Joe played different sports and one required twice as much energy, how would you analyze their energy expenditure?
  5. How would you calculate the area of a triangular garden with a base of 12 m and height of 5 m?

Tip: For sums of sequences, try using the formula for arithmetic series, as it’s quick and efficient!

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Math Problem Analysis

Mathematical Concepts

Arithmetic operations
Algebraic equations
Geometry (area calculation)
Number theory (summing whole numbers)
Unit conversion

Formulas

Sum of an arithmetic series: S = (n/2) * (a + l)
Area of a rectangle: Area = length * width
Conversion between miles and kilometers

Theorems

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Suitable Grade Level

Grades 6-8