Word Problem on Money ( Equation solving )

Examples 

Hailey was selling tickets for a school play. She sold 10 more adult tickets than children tickets and she sold twice as many senior citizen tickets than children tickets. If Hailey sold58 tickets total, how many of each type did she sell?

 

Solution 

 

 

Ratios and Proportions : Word Problem

 Example

 

It takes John 5hours to paint 2 rooms. How long will it take to paint 5 rooms?

 

Solution 

 

Ratios and Proportions : Word Problem

 Example

 

Samantha owns a farm. For every 3 goats there are 7 cows. If she has a total of 39 goats, how many total cows does Samantha have? 

 

Solution

 

Grade 9 : Math 1 - Indroductory Activity on Grade 8 Skills ( Worksheet with worked Answers)

 1) What is the value of x in the equation shown below?

            0.25x + 7 = 4(x-2)

Solution

 

 

2) What is the rate of change of the linear function that has a graph that passes through the points (2,9) and (-1,3) ?

Solution 

 

Here they asked us to find the rate of change which means slope

also, they have given two pints

When two points are given,

the formula for the slope is,

3) What values of x satisfies the equation -4x -2 / 3 = -6

 

Solution

 

 

4) Which scenario would most likely to show a negative association between the variables?

 

a) The height of a tree x , and the amount of time it takes to climb to the top of the tree y

b) the number of people in the mall x , and the number of cars in the parking lot y

c) miles traveled in a car  x and the amount of gasoline used y

d) time spend reading a book x , and the number of pages left to read y

Solution

Positive association

Two variables have a positive association when the values of one variable tend to increase as the values of the other variable increase.

 

Negative association

Two variables have a negative association when the values of one variable tend to decrease as the values of the other variable increase.

 

Option a,b,c are all positive association because if x value increases y also increases and if x decreases y value also decreases.

 

Ans is option d) time spend reading a book x , and the number of pages left to read y is negative association 

 

because 

here,  x increases y gets decreases that is,

as we spend more time the pages left decreases

 

5) Mr. Jones determined that the equation y = 98 - 16/5 x could be used to predict his students' unit test scores,
based on the number of days, x, a student was absent during the unit.
what was the meaning of the y-intercept of the function?

A. A student who was not absent during the unit should score about 98.
B. A student who was not absent during the unit should score about 94.5.
C. A students test score should score increase by about 3.2 points for each day the student is absent.
D. A student test score should decrease by 3.2 points for each day the student is absent.

 

Solution

 

Given,

x = number of days absent , y = student unit score

y = 98 - (16/5) x 

 y-intercept means we have to find y when x=0 in the given equation

x=0 means, No absent days

 when x= 0 ,

y = 98 -(16/5) * 0

   = 98 - 0

   = 98

When x = 0 , y = 98 that is

unit score =98 and No absent days

 

Hence answer is A) A student who was not absent during the unit should score about 98.

 

6) In which choice is y a function of x?

 

A)  (1,3) (3,4) (4,5) (5,6)

B)  (2,0) (2,3) (4,5) (6,7)

C)  (2,5) (4,8) (6,10) (2,12)

D)  (6,2) (4,1) (6,8) (8,10) 

 

Solution

 

y a function of x means , y=f(x)

here, y = output and x = input

y is a function of x says that,

input(x) must be unique values

and each input should have one output value

lets consider option

B)  (2,0) (2,3) (4,5) (6,7)   [ x has two same values which is 2]

C)  (2,5) (4,8) (6,10) (2,12) [x has two same values which is 2

D)  (6,2) (4,1) (6,8) (8,10) [x has two same values which is 6]

 

Hence answer is option A) (1,3) (3,4) (4,5) (5,6)

 which has unique x values and each x has y values. 

 

7) A company charges $211.25 for 5 trees and 15 shrubs.The company charges 15.25 more for a tree than a shrub. how much does each shrub cost? 

Solution

 

Given,

          5 Trees + 15 Shrubs = $211.25 

               Tree = 15.25 + Shrub

Now replace Tree by 15.25 + Shrub in the first equation

      5 ( 15.25 + Shrub) + 15 Shrubs = 211.25

     

            76.25 + 5 Shrubs + 15 Shrubs = 211.25

                  76.25 + 20 Shrubs = 211.25

                               20 Shrubs = 211.25 - 76.25

                                20 Shrubs = 135

                                 1 Shrub = 135/20 = 6.75

Hence Each shrubs cost $6.75

 

8) In which choice is y a non linear function of x?

 

A)  x    0     2     4     6     8   

     y   24   18    12    6     0

B)  x    0     2     4     6     8   

     y   24   18    13    9     6

 

C)  x    0     2      4      6      8   

     y   24    21    18    15     12

 

D)  x    0     2      4      6      8   

     y   24    22    20    18     16

 

Solution

 

To find whether y is a non linear function of x , we have to find the difference between y values.

If the difference between y values are same then y is a non linear function

 

Answer : B)  , lets find the difference between y values

 y  24   18    13    9     6

24-18 = 6

18 - 13 = 5

13 - 9 = 4

9 - 6 = 3   [ the values we got here are difference]

9) Which equation best models the data shown in the scatterplot below?

 

 

 

 

 

 

A) y = 3x+10

B) y=3x+60

C) y=4x+5

D) y=4x+35

 

Solution

 

 

Hence Answer is D) y = 4x+35

10) A car rental company charges $34 per day for a rented car and $0.50 for every mile driven. A second rental company charges $20 per day and $0.75 for every mile driven. What is the number of miles at which both companies charge the same amount for a one-day rental?

 

Solution 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Hence Answer is 56 miles

 

Grade 10 : CBSE : Mathematics Sample question paper (MCQ) with detailed answer - Term 1

 Class - X

Mathematics

Sample Question Paper - Term 1

1) The ratio of LCM and HCF of the least composite and the least prime numbers is _____

Solution

Least composite number = 4

Least prime number = 2

LCM of the least composite and the least prime numbers  

that is, LCM of 4 and 2 is 4

HCF of 4 and 2 is 2

ration of LCM and HCF = 4:2 = 2:1

Hence the answer is 2:1

2) The value of k for which the lines 5x+7y=3 and 15x+21y = k coincide is _______

Solution

consider the first equation 5x+7y=3

 observe the second equation, if we multiply the first equation by 3 then we will get the left-hand side of the second equation

that is, (5x+7y=3) * 3 

gives,  15x + 21y = 9

now let's compare the above equation with the second equation, 

we got k = 9

Hence the value of k is 9

Note: When two lines are coinciding with each other, then there could be no intercept difference between them. For example, 5x+7y=3 and 15x+21y = 9  are coinciding lines.

3) A girl walks 200m towards the East and then 150m towards the North. The distance of the girl from the starting point is _____

Solution 

Hence the distance of the girl from the starting point is 250m

4) The lengths of the diagonals of a rhombus are 24cm and 32cm, then the length of the altitude of the rhombus is _____

Solution

In Rhombus, all the sides are equal

Diagonals of the Rhombus are Perpendicular bisectors of each other.

AC is perpendicular to BD

so, OB = BD/2 = 32/2 = 16

      OA = AC/2 = 24/2 = 12

Now, in Right angle Triangle OAB , 

By Pythagorus theorem 

AB^2 = OA^2 + OB^2

          =  12^2 + 16^2

          = 144 + 256

AB^2 = 400

AB ( Base ) = 20

Area of Rhombus = 1/2 * diagonal 1 * diagonal 2

                              = 1/2 * 24 * 32  = 12 * 32

                              =  384 cm^2

Area using base and height :

 

Area of Rhombus = Base * Height

           384             =  20 * Height

height = 384/20 = 19.2Cm

Hence the altitude of the Rhombus = 19.2cm

5) Two fair coins are tossed. What is the probability of getting at the most one head?

Solution

Possible outcomes (Sample space S) = { HT , TT, HH , TH }

Number of possible outcomes [ n(S) = 4 ]

Favourable Outcome = Getting at the most one head = Outcomes with NO head + Outcome with 1 head

= { HT , TT , TH }

Number of favourable outcomes = 3

Probability = Number of favourable outcomes / Total number of outcomes

Probability of getting at the most one head = 3 / 4 or 3:4

Hence the answer is 3/4

6) ΔABC~ΔPQR. If AM and PN are altitudes of ΔABC and ΔPQR respectively and AB^2 : PQ^2 = 4 : 9, then AM:PN =

Solution

Given,  

               AB^2 : PQ^2 = 4 : 9

implies     AB^2 / PQ^2 = 4 / 9

               (AB/PQ)^2 = 2^2/3^2

                AB/PQ = 2/3

Also given, Triangle ABC and Triangle PQR are similar triangles then

Ratio of their altitudes = ratio of their sides

 AM : PN = AB : PQ

that is , AM : PN = 2 : 3

Hence the answer is 2 : 3