Math Problem Statement

solve

Solve the given mathematical problems in the uploaded image.

Solution

Let’s analyze and solve the mathematical problems in the image step by step.

Question 9

Task: Using the digits 5, 8, and 9, find all distinct numbers that are divisible by 5. Calculate the sum of the quotients when these numbers are divided by 5.

Solution:

  1. Numbers that can be formed using 5, 8, and 9:
    • We can form 3-digit numbers where the last digit must be 5 (to ensure divisibility by 5). The possible numbers are:
      • 895
      • 985
  2. Dividing these numbers by 5:
    • 895÷5=179895 \div 5 = 179
    • 985÷5=197985 \div 5 = 197
  3. Sum of the quotients:
    • 179+197=376179 + 197 = 376

Answer: 376


Question 10

Task: Find the number such that when multiplied by 6, the result is equal to the sum of 276 and 456.

Solution:

  1. Sum of 276 and 456:
    • 276+456=732276 + 456 = 732
  2. Solve for xx in the equation:
    • 6x=7326x = 732
    • x=7326=122x = \frac{732}{6} = 122

Answer: 122


Question 11

Task: There is 210 kg of cabbage from one field and 3 times that amount from another field. These cabbages are distributed equally into 8 baskets. How many kilograms of cabbage are in each basket?

Solution:

  1. Cabbage from the first field: 210kg210 \, \text{kg}
  2. Cabbage from the second field: 3×210=630kg3 \times 210 = 630 \, \text{kg}
  3. Total cabbage:
    • 210+630=840kg210 + 630 = 840 \, \text{kg}
  4. Distribute equally into 8 baskets:
    • 8408=105kg per basket\frac{840}{8} = 105 \, \text{kg per basket}

Answer: 105 kg


Final Summary:

  • 9: 376
  • 10: 122
  • 11: 105 kg

Would you like detailed explanations or clarification for any step?


Related Questions:

  1. How many unique numbers can you form using three digits (5, 8, 9) if repetition is not allowed?
  2. What is the least common multiple (LCM) of 276 and 456?
  3. What is the total weight of the cabbage if the fields are combined, and how can it be distributed if there are 10 baskets instead of 8?
  4. What is the result if you divide the sum of 276 and 456 by a number other than 6?
  5. How can you systematically list all permutations of a set of three digits?

Tip: When solving for quotients or remainders, double-check divisibility rules to ensure accuracy!

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Math Problem Analysis

Mathematical Concepts

Divisibility
Arithmetic Operations
Multiplication
Division
Sum of Numbers

Formulas

Divisibility rule for 5
Sum of numbers formula: Total = A + B
Division formula: Quotient = Dividend / Divisor
Multiplication formula: Product = Multiplier × Multiplicand

Theorems

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Suitable Grade Level

Grades 6-8