Solving multi-step equations 1) p-1=5p+3p-8
2 answers:
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<h2>Systems of Equations Word Problems</h2>
To solve these questions, we can translate key words into operations:
- <em>Difference</em> = subtract
- <em>Twice</em> = double
- <em>Less than</em> = subtract
We're given:
- Difference of Annie's age and twice Carl's age is 22
- Annie's age is 13 less than 3 times Carl's age
There are two variables given two us: Annie's age and Carl's age.
- Let Annie's age be equal to <em>x.</em>
- Let Carl's age be equal to <em>y</em>.
Translate the given information into two equations:
- Difference of Annie's age and twice Carl's age is 22
⇒
- Annie's age is 13 less than 3 times Carl's age
⇒
Now, we can substitute the fist equation into the second one to solve for <em>y</em>:
Now, substitute <em>y</em> back into the second equation to solve for <em>x</em>:
Therefore, Grandma Annie is 92 years old.
We need to find the number of integers between 100 and 500 that can be divided by 6, 8, or both. Now, to do this, we must as to how many are divisible by 6 and how many are multiples of 8.
The closest number to 100 that is divisible by 6 is 102. 498 is the multiple of 6 closest to 500. To find the number of multiple of 6 from 102 to 498, we have
We can use the same approach, to find the number of integers that are divisible by 8 between 100 and 500.
That means there are 67 integers that are divisible by 6 and 50 integers divisible by 8. Remember that 6 and 8 share a common multiple of 24. That means the numbers 24, 48, 72, 96, etc are included in both lists. As shown below, there are 16 numbers that are multiples of 24.
Since we counted them twice, we subtract the number of integers that are divisible by 24 and have a final total of 67 + 50 - 16 = 101. Hence there are 101 integers that are divisible by 6, 8, or both.
Answer: 101
The closest number to 100 that is divisible by 6 is 102. 498 is the multiple of 6 closest to 500. To find the number of multiple of 6 from 102 to 498, we have
We can use the same approach, to find the number of integers that are divisible by 8 between 100 and 500.
That means there are 67 integers that are divisible by 6 and 50 integers divisible by 8. Remember that 6 and 8 share a common multiple of 24. That means the numbers 24, 48, 72, 96, etc are included in both lists. As shown below, there are 16 numbers that are multiples of 24.
Since we counted them twice, we subtract the number of integers that are divisible by 24 and have a final total of 67 + 50 - 16 = 101. Hence there are 101 integers that are divisible by 6, 8, or both.
Answer: 101