Grade 9 : Math : Word problem on Function

 The function  models the population of rabbits on a farm after   with no removal. The function  models the number of rabbits removed from the population after . Which function,  , models the total number of rabbits on the farm after ?

Solution

f(x) = h(x) + g(x)

that is,

Total models population of rabbits with NO removal = models of rabbits removed from the population after x months + Total number of rabbits on the farm after x months

Let's substitute the given values in the above equation

Hence answer is h(x) = 2(2.0)^x

Grade 9 : Math : Word problem on Linear inequivalities

 A man bought x boxes of doughnuts for $3.49 each, he paid with a $50 bill and received the correct amount of change. If he received more than $10 but less than $20, which inequalities represent the number of boxes of doughnuts he could have bought?

A. 9 ≤ x ≤ 11
B. 8 ≤ x ≤ 12
C. 8 ≤ x ≤ 11
D. 9 ≤ x ≤ 12

Solution

By the given information,

Received amount = total amount paid - x*3.49

                         = 50 - 3.49x

10 ≤ 50 - 3.49x ≤ 20

Hence option A) 9 ≤ x ≤ 11 is the answer.

Math : Grade 9 : Word Problem on Rates

 A pilot flew from airport A to airport B at a rate of 100 km/hr and flew 

back from airport B to airport A at 120 km/hr. The total time it took was 
11 hours. How far is it from airport A to airport B?

Solution

Let's assume, the distance between the airports = d km

Formula : rate = distance / time

airport A to B

        given, rate = 100 km/hr

                  time = t1 (let's assume time take to reach from airport A to B)

                  distance = d

              100 = d/t1   (substitute values in the formula)

airport B to A

   given, rate = 120 km/hr

                  time = t2 (let's assume time take to reach from airport B to A)

                  distance = d

 

                 120 = d/t2  (substitute values in the formula)

also given total time (that is, from airport A to B and airport B to A)= 11 hours

which is      t1+t2 = 11

Hence, the distance between airports = 600 km

Math : Word problem on Ratios/proportions

Set up and solve the proportions

The park ranger stocks the children's fishing pond, keeping a ratio of 4 sunfish to 3 perch. If he puts 300 sunfish into the pond, how many perch should be put into the pond?

Solution

given, 4Sunfish to 3 perch 

that is 4/3

we have to find 300 Sunfish to how many perch (x)

since its a ratio, we can equate those two

Hence he should put 225perch into the pond

Grade 9 : Word problem on Linear equation

 We can translate word problems into equations to solve

1. Find two consecutive integers whose sum is 45

Solution

let us assume one of the integer is x

since its two consecutive integers, the second integer must be x+1

also given, their sum is 45

that is  x + (x+1) = 45

           2x + 1 =45

              2x = 45 -1 =44

              2x =44

              x = 44/2

              x =22

one of the integer is 22

next integer is 22+1 = 23

let check whether if we add these two integers we will be getting 45

22+23 = 45

hence the two consecutive integers are 22 and 23

Grade 9 : Math : Word Problem

Water is being pumped into a 10-foot-tall cylindrical tank at a constant rate.

• The depth of the water is increasing linearly.
• At 1:30pm, the water depth was 2.4 feet.
• It is now 4:00pm and the depth of the water is 3.9 feet.

What will the depth (in feet) of the water be at 5:00 pm?

Solution

First lets write the given statement in points ( time, water depth in feet)

Given,

At 1:30pm, the water depth was 2.4 feet

which means (1.5 , 2.4 )

 [ 1.30 pm which means 1 1/2 so, we are writing it as 1.5]

also given, 

It is now 4:00pm and the depth of the water is 3.9 feet.

that is ( 4 , 3.9 )

Now we got two points (x1,y1) = (1.5,2.4)

                                  (x2,y2) = (4,3.9)

Slope (m)= y2 - y1 / x2 - x1

               = 3.9 - 2.4 / 4 - 1.5

               = 1.5 / 2.5

                    m  = 0.60

Every hour water level increases 0.60 feet

we have to find the depth (in feet) of the water be at 5:00 pm

we found m=0.60

lets take one of the given point (1.5,2.4) (x1,y1)

we have to find y when x=5(5pm)

y - y1 = m(x-x1)

y - 2.4 = 0.60(5-1.5)

y - 2.4 = 0.60(3.5)

y-2.4 = 2.1

y = 2.4 + 2.1

    = 4.5 feet

Hence the depth (in feet) of the water be at 5:00 pm is 4.5ft