Please help with these.?

Question

1) At a certain time in a deer park there are 45 heads and 146 legs. Counting boththe deer and human visitors how many deer and human visitors were there?

2)Grandpa's age in yrs is equal to his dog's age in months. If the difference in the ages is 55yrs' find the age of each?

3)A chemist has one solution in which there is 50%acid and a 2nd one with 25%acid. How much of each should be there to make a 40%acid solution?

4) On a school picnic a group of students agreed to pay equall for the use of a pull boat and pay Rs10 each. If there are 3 more students in the group each would have to pay Rs 2 less. How many students were there?

Answer 1

Let there be x human visitors and 45-x deers
total no of legs
=2x+4(45-x)
=2x+180-4x
=-2x+180
But it is given that the total no of legs are 146
Therefore
-2x+180=146
or,-2x=146-180=-34
x= -34/-2=17
Therefore there were 17 visitors and (45-17 or)28 deers
2)Let Grandpa's age be x years.Hence the dog's age is x months or x/12 years
Therefore,
x-x/12=55
12x-x=660 [multiplying both sides by 12]
11x=660
x=660/11=60
Therefore Grandpa's age is 60 years and the dog's age is 60 months or 5 years
3)Let x litres of 25%acid be mixed with 1 litre of 50% acid to make 1+x litre of 40% acid
By the problem,
0.50*1+0.25x=0.40(1+x)
=>0.50+0.25x=0.40+0.40x
=>0.25x-0.40x=0.40-0.50
=> -0.15x= -0.10
=> x= -0.10/-0.15
=>2/3 litre
Therefore 2/3 litres of the second solution should be mixed with 1 lit of the first solution to get 40% solution
The ratio of first solution to the 2ns one
=1:2/3
=3:2 [multiplying both the ratios by 3]
4)Let there be x students
Therefore,the rent of the pool boat=10x
Again if there were 3 more students,they were required to pay Rs 8 only
therefore,
8(x+3)=10x
=> 8x+24=10x
=>8x-10x= -24
=> -2x= -24
=> x= -24/-2=12
ltherefore,there were 12 students

Answer 2

146 = 2h + 4(45 - h), so 146 = 180 - 2h, or 2h = 34, so h = 17
17 humans, and 28 deer

g = 12d, and g = 12(g - 55), so 12g - 660 = g, or 11g = 660, g = 60, d= 5

.5x + .25(100 - x) = .4*100, so .25x = 40 - 25 = 15, and x = 60, so if the total amount of solution is S, 60% * S is 50% acid and 40% * S is 25% acid.

10x = 8 (x+3), so 10x = 8x + 24, and 2x = 24, so x =12
there were 12 students

Answer 3

Let x = number of humans
Then 45-x = number of deer
2x = number of human feet
4(45-x) = number of deer feet
2x+4(45-x) =146
2x+180 -4x = 146
-2x = - 34
x= 17 = number of humans
45-17 = 28 = number of deer

x= Grandpa's age in years
x = Dog's age in months
(12x -x)/12 = 55
11x = 12*55
x = 60 = Grandpa's age in years
x = 60 months = Dog's age in months

x=number of students originally
10x = cost of boat
(x+3)8 = 10x
8x +24 =10x
2x =24
x = 12 students originally

x/10 +3+ new number in group

Answer 4

1)a=human visitors, b=deer

a + b=45 } -2a -2b = -90 } 2b=56 <=> b=28
2a+4b=146 } 2a+4b=146 }

So a=45-28=17.
17 human visitors and 28 deers.

2) a=Granpa's age b=dog's age

a=12b } a=12b } a=60
a-b=55 } 11b=55 } b=5

Grandpa is 60 yo and dog is 5 yo.

3) Can't find a solution.

4)n=number of students
10n=8(n+3) <=> 10n=8n+24 <=>2n=24 <=> n=12
At first there were 12 students.