saome math help please!?

Question

these r some questions from my long math home work
please help as much as u can
thanx
just a little explnation(working) wuuld be helpful

1. A piece of wood is cut into 3 pieces, A B and C in the ratio 2:3:5. if C is longer than B by 8 cm, find the legth of the stick.

2.Working 8 hours a day,48 men can complete a job in 1 week.How many men workin 6 hours a day would it take to complete the job in 16 days?

3. If 125kg of food is sufficient for24 soldiers for 5 days, how will the food last for 30 soldiers?

just a little explnation(working) wuuld be helpful

Answer 1

1.) A piece of wood is cut into 3 pieces, A B and C in the ratio 2:3:5. if C is longer than B by 8 cm, find the legth of the stick.

Using the ratio given, we can say that 5 lengths of B would equal 3 lengths of C.
3C = 5B
The second part of the problem can be rewritten:
C = B+8

Now use substitution:
3(B + 8) = 5B
3B + 24 -3B = 5B - 3B
24/2 = 2B/2
12 = B
C = B + 8 = 20

3 lengths of A = 2 lengths of B
3A = 2B
3A = 2 * 12
3A/3 = 24/3
A = 8
A + B + C = length of stick
8 + 12 + 20 = length of stick
the stick is 40 cm.

Alternative:
Once you know that C = 20, you can use the ratio: 2:3:5 and rewrite it so that:
A + B = C
If A + B + C = length, then substitite C for A + B.
C + C = length
20 + 20 = 40 cm.

2.) Working 8 hours a day,48 men can complete a job in 1 week.How many men workin 6 hours a day would it take to complete the job in 16 days?

Rewrite the first portion to man-hours:
48 men complete a job in 1 week (7 days) working 8 hours a day.
48 men complete a job in 56 hours
Therefore, the job requires 2688 man-hours.

6 hours a day * 16 days = 96 total hours.
2688 man-hours / 96 hours = 28 men

3.) 125kg of food is sufficient for24 soldiers for 5 days, how will the food last for 30 soldiers?

125 kg of food feeds 24 soldiers for 5 days.
125 kg of food therefore feeds 120 soldiers in 1 day (multiply 24 * 5)
120 solders/day / 30 soldiers = 4 days of food.