Please help..?!?

Question

-Find three consecutive even integers such that the sum of the first two is greater than 27 and the sum of the last two is less than 39.

-An oak tree is 6 times as old as a pine tree and an elm tree is 6 years younger than the oak tree. In 3 years, the age of the elm will be 3 times the age of the pine. How old is the oak tree now?

-The ratio of the present ages of two museums is 3 to 5. Twelve years ago, the sum of their ages was less than 56 years. Find the possibilities for the present age of the younger museum.

-Cities A and B are located on an east-west highway at a distance of 244 mi from each other. A truck left City A at 8:00 A.M. driving 47 mi/h toward City B. A car left City B at 10:00 A.M. traveling 53 mi/h toward City A. At what time did the car pass the truck?

Answer 1

x+2 = y
y+2 = z

x+y>27, x + (x+2) > 27, 2x + 2 > 25, 2x > 29, x > 12.5
y+z<39, z + (z-2) < 39, 2z - 2 < 39, 2z < 41, z < 20.5

Valid answers are [14,16,18] or [16,18,20]
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T = oak tree age, P = pine tree age, E = elm tree age
T = 6P
T-6 = E
3(P+3) = (E+3)

Put the first equation into the left side of the third equation
Put the second equation into the right side of the 3rd equation
3( T/6 + 3) = (T-6 + 3)
(T/2 + 9) = T - 3
12 = T/2
T = 24
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Answer 2

Let A, B and C be the three consecutive even integers. That means B = A +2 and C = B + 2 = A + 4

A + B > 27 - first condition
B + C < 39 - second condition.

Sum of two even integers has to be even. So, the lowest value for A + B = 28.

Similarly the highest value for B + C = 38

A + B = A + A + 2 = 28 or more but less than 36

B + C = B + B + 2 = A + A + 4 + 2 = 38 or less

2A + 2 = 28 to 36 or A = 26 to 34 / 2 = 13 to 17 range

Similarly 2A + 6 = 38 or less

2A = 32 or less and A = 16 or less

Since A = 16 satisfies both the conditions, let us see whether our check is OK.

A + B = 16 + 18 = 34
B + C = 18 + 20 = 38

So, our solution is acceptable.

I will do the last problem and leave others for you to try out.

At 10 AM, the truck will be at a distance of 94 miles from A. So the distance between the truck and the car at that point is 244-94 = 150 miles.

Now let t be the time that they cross each other. 47.t = 150 - 53.t or 100.t = 150 and t = 1.5 hours.
That is the car passed the truck at 11:30

Answer 3

1) the numbers are 14,16,18 or 16,18,20