1. List 2 pairs of numbers that fit the following description: Show your work for full marks • A pair of numbers has a sum of 90. • The FIRST NUMBER is a MULTIPLE of 2. • The SECOND NUMBER is a FACTOR of 40.
Pair 1:
First number = 20 (a multiple of 2)
Second number = 10 (a factor of 40)
Sum: 20 + 10 = 30
Pair 2:
First number = 40 (a multiple of 2)
Second number = 5 (a factor of 40)
Sum: 40 + 5 = 45
To find pairs of numbers that fit the given description, we need to find numbers that satisfy the following conditions:
Condition 1: The pair of numbers has a sum of 90.
Condition 2: The first number is a multiple of 2.
Condition 3: The second number is a factor of 40.
Let's analyze each condition and find valid pairs:
Condition 1: The pair of numbers has a sum of 90.
This condition means our pair of numbers must add up to 90.
Condition 2: The first number is a multiple of 2.
To satisfy this condition, the first number must be any even number.
Condition 3: The second number is a factor of 40.
To satisfy this condition, the second number must be a divisor of 40.
Considering all three conditions, let's find two pairs of numbers:
Pair 1:
Let's choose the first number to be 40, which is a multiple of 2 and satisfies condition 2.
To obtain the second number, we need a factor of 40. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.
Let's choose the second number as 50, which is a factor of 40 and satisfies condition 3.
Pair 2:
Let's choose the first number to be 10, which is a multiple of 2 and satisfies condition 2.
To obtain the second number, we need a factor of 40. Let's choose the second number as 4, which is a factor of 40 and satisfies condition 3.
So, two pairs of numbers that fit the given criteria are:
Pair 1: (40, 50)
Pair 2: (10, 4)
To find pairs of numbers that fit the given description, we need to follow these steps:
Step 1: Determine the multiples of 2.
The multiples of 2 are:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, ...
Step 2: Determine the factors of 40.
The factors of 40 are:
1, 2, 4, 5, 8, 10, 20, 40
Step 3: Find pairs of numbers that have a sum of 90.
We need to look for pairs of numbers from the multiples of 2 and factors of 40 whose sum is 90:
(52,38), (46,44), (40,50), (34,56), (28,62), (22,68), (16,74), (10,80), (4,86)
Therefore, two pairs of numbers that fit the given description are:
1. (52, 38): The first number, 52, is a multiple of 2, and the second number, 38, is a factor of 40.
2. (46, 44): The first number, 46, is a multiple of 2, and the second number, 44, is a factor of 40.