Max was on vacation twice as long is Jared and half as long as Wesley. The boys were on vacation a total of three weeks. How many days with each boy on vacation?
Answers
21 total days of vacation.
Max + Jared + Wesley = 21 days
(Let's use the first letter of their name to represent their vacation time)
M + J + W = 21 [This is the equation we'll be coming back to]
Now, we can use the clues given in the question to have an equation for each variable/boy.
Max was on vacation twice as long as Jared. We can interpret this as M= 2J Max was on vacation only half as long as Wesley. We can interpret this as M = (1/2)W.
So far we have these three equations: M + J + W = 21M = 2J M = (1/2)W
To have an equation for each individual boy, we must rearrange the last two equations in the list.
First, M = 2J.
Divide both sides by 2
M/2 = 2J/2
(1/2)M = J
Second, M = (1/2)W
Multiply both sides by 2
2M = W
New equations:
M + J + W = 21 [From the old list]
J = (1/2)W
W = 2M
Now we can substitute the last two equations into the first one.
M + J + W = 21
M + (1/2)W + 2M = 21
[Combine Like Terms]
(7/2)M = 21
Then, solve for M (Max's vacation days):
Multiply both sides by 2/7
M = 6
Now we know Max was on vacation for 6 days.
If Max was on vacation twice as long as Jared, that means Jared was on vacation HALF as long as Max.
So...
J = (1/2)M
J = (1/2) * 6
J = 3
Jared was on vacation for 3 days
Wesley was on vacation twice as long as Max so... W = 2M
W= 2*6
W = 12
Wesley was on vacation for 12 days.
Let's double check our answer:
M + J + W = 21 days6 + 3 + 12 = 21
The numbers work out so the math is correct. Hope this helps and makes sense!
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Answer:
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Step-by-step explanation:
-5x(x^2)=-5x^3
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All together: -5x^3 - 10x^2 - 15x
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B.
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Answer:
2/405
Step-by-step explanation:
Simplify the following:
(-2)/9×((-1)/3×1/3)/5
(-1)/3×1/3 = (-1)/(3×3):
(-2)/9×((-1)/(3×3))/5
(-1)/(3×3)×1/5 = (-1)/(3×3×5):
(-2)/9×(-1)/(3×3×5)
(-2)/9×(-1)/(3×3×5) = (-2 (-1))/(3×3×5×9):
(-2 (-1))/(3×3×5×9)
3×3 = 9:
(-2 (-1))/(9×5×9)
9×5 = 45:
(-2 (-1))/(45×9)
45×9 = 405:
(-2 (-1))/405
-2 (-1) = 2:
Answer: 2/405