The number of weeks after which they both have volunteered the same number of hours is 4 weeks. The amount volunteering time they'd have volunteered till that week is 16 hours.
How to form mathematical expression from the given description?
You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
Given that:
- Cyrus has already volunteered 8 hours when Adrian begins to volunteer
- Adrian volunteer 4 hours per week
- Cyrus volunteer 2 hours per week.
Let the number of weeks after which they both have volunteered the same number of hours be 'w' weeks.
Now, as Adrian volunteer 4 hours per week, then in w weeks, he'd have volunteered [tex]4 \times w[/tex] hours.
Also, as Cyrus already volunteered 8 hours, and then for w weeks, he volunteered 2 hours per week, so the number of hours he volunteered is: [tex]2 \times w + 8[/tex]
We had assumed that after w weeks, their volunteer time is same, so we can equate these amount of volunteering hours, as shown below:
[tex]4\times w= 2\times w + 8\\4w = 2w + 8[/tex]
(sign of multiplication is often hidden if there are non numeric symbols and numbers being multiplied are written together)
Subtracting 2w from both the sides, we get:
[tex]4w -2w = 8\\(4-2)w = 8\\2w = 8[/tex]
Dividing both the sides by 2, we get w on one side, rest of the constants on the other side, as:
[tex]\dfrac{2w}{2} = \dfrac{8}{2}\\\\w = 4[/tex]
Thus, the number of weeks after which they both have volunteered the same number of hours is w = 4 weeks.
Now, evaluating any of those expressions to get the number of hours each of them volunteered till 4th week:
[tex]4w |_{w=4} = 4 \times 4 = 16 \: \rm hours\\2w +8|_{w=4} = 2(4) + 8 = 8+8 = 16 \: \rm hours[/tex]
(see, these are equal amount of time).
Thus, the number of weeks after which they both have volunteered the same number of hours is 4 weeks. The amount volunteering time they'd have volunteered till that week is 16 hours.
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