<span>1. 2m + 4
2. w(w+7) = 60
3. 0.2 mph
To solve the first question, look at the statement:
"Zach is 4 years older than twice his sister Maya’s age"
We'll use "m" for Maya's age.
"Zach is 4 years older ..."
So your expression will have a "+ 4" in it. Write that down, giving:
+ 4
"than twice his sister Maya's age"
OK, we're using "m" for Maya's age. And the "twice" means times 2. So we have 2m to represent twice Maya's age. Add that to the expression we have so far.
+ 4 + 2m
Now, of the 4 options you've allowed to pick from, do any of them look like they can match + 4 + 2m?
2m + 4: This looks like a match. Just swap the "+4" and "2m".
4m + 2: Nope, 4m doesn't match what we've got. Bad choice
m + 4: Nope, I don't see a 2m anywhere. Bad choice.
2m: Got the 2m, but where's the +4? Also a bad choice.
So 2m + 4 is the only reasonable choice and is the correct answer.
Now for the 2nd question.
The area of a rectangle is 60 in² and the length of the rectangle is 7 in. longer than the width.
The area of a rectangle is width times length, so let's use w and l to represent those values, and a to represent area. giving us
a = wl
We know that the length is 7 inches longer than the width, so let's make that expression too.
l = w + 7
Now let's substitute the expression we made for l into the formula we have for the area of a rectangle.
a = wl
a = w(w+7)
Finally, since we know the area (60 square inches), let's substitute that into the formula as well.
60 = w(w+7)
And now, let's see if what we've done matches any of the possible choices.
w(w+7)=60: Looks good. Just got the equations on the opposite sides of the equal sign. Can swap them easily enough.
w + 7 = 60: Looks like a w is missing. Bad choice.
w + 7w = 60: All the right numbers and letters are there. But where did that multiply by 7 come from? Bad choice.
7w = 60: Not only do we still have that strange multiply by 7, we're also missing a w. Bad choice.
So for your second question, only "w(w+7) = 60" makes any sense.
Finally, for your third question, we have "A mail truck traveled 82 miles in 412 hours." ... "To the nearest tenth, what was the average speed of the mail truck?"
For this one, you simply divide the distance by the time. So we have 82 miles divided by 412 hours.
82 / 412 = 0.199 miles per hour. Rounds off to 0.2 miles per hour.
On a personal note, I would suggest that you double check what your typed for the 3rd problem. 412 hours is over 17 days long. And for the word problem you've presented, that is a rather absurd number and makes me think that you typed something wrong there. But regardless of what you typed, the method of solving the problem is the same, simply divide the distance by the time.</span>
