WORD PROBLEMS ON LINEAR EQUATIONS
Problem 1 :
If the numerator of a fraction is increased by 2 and the denominator by 1, it becomes 1. In case, the numerator is decreased by 4 and the denominator by 2, it becomes 1/2. Find the fraction.
Solution :
Let x/y be the fraction.
Given : If the numerator is increased by 2 and the denominator by 1, the fraction becomes 1.
(x + 2)/(y + 1) = 1
(x + 2)/(y + 1) = 1
x + 2 = y + 1
x - y = -1 ----(1)
Given : In case the numerator is decreased by 4 and the denominator by 2, the fraction becomes 1/2.
(x - 4)/(y - 2) = 1/2
2(x - 4) = 1(y - 2)
2x - 8 = y - 2
2x - y = 6 ----(2)
Solving (1) and (2), we get
x = 7 and y = 8
Hence, the fraction is 7/8.
Problem 2 :
A park charges $10 for adults and $5 for kids. How many many adults tickets and kids tickets were sold, if a total of 548 tickets were sold for a total of $3750 ?
Solution :
Let x be the no. of adult tickets and "y' be the no. of kids tickets sold.
Given :A total of 548 tickets were sold.
x + y = 548 ----(1)
Given : Cost of each adult ticket is $10 and kid ticket is $5 and tickets were sold for a total of $3750.
10x + 5y = 3750
2x + y = 750 ----(2)
Solving (1) & (2), we get
x = 202 and y = 346
Hence, the number of adults tickets sold is 202 and kids tickets is 346.
Problem 3 :
A number consists of three digits of which the middle one is zero and the sum of the other digits is 9. The number formed by interchanging the first and third digits is more than the original number by 297.Find the number.
Solution :
Let x0y be the three digit number. (As per the given information, middle digit is zero).
Given : The sum of the other digits is 9.
x + y = 9 ----(1)
By interchanging the first and third digits, the number we get is
y0x
Given : The number formed by interchanging the first and third digits is more than the original number by 297.
y0x - x0y = 297
(100y + x) - (100x + y) = 297
100y + x - 100x - y = 297
-99x + 99y = 297
-x + y = 3 ----(2)
Solving (1) & (2), we get
x = 3 and y = 6
x0y = 306
Hence the three digit number is 306.
Problem 4 :
A manufacturer produces 80 units of a product at a cost of $22000 and 125 units at a cost of $28750. Assuming the cost curve to be linear, find the equation of the cost curve and then use it to estimate the cost of 95 units.
Solution :
Since the cost curve is linear, its equation will be
y = Ax + B.
(Here y = Total cost, x = no. of units)
Given : The total cost of 80 units of the product is $22000.
22000 = 80A + B
80A + B = 22000 ----(1)
Given : The total cost of 125 units of the product is $28750.
28750 = 125A + B
125A + B = 28750 ----(2)
Solving (1) and (2), we get
A = 150 and B = 10000
Then, the equation of the cost curve is
y = 150x + 10000 ----(3)
Estimate the cost of 95 units :
Substitute x = 95 in (3).
y = 150(95) + 10000
= 14250 + 10000
= $24,250
Problem 5 :
Y is older than X by 7 years. 15 years back X's age was 3/4 of Y's age. Find the present their present ages.
Solution :
Let x be the present age of X and y be the present age of Y.
Given : Y is older than X by 7 years.
y = x + 7 ----(1)
15 years back :
X's age = x - 15
Y's age = y - 15
Given : 15 years back X's age was 3/4 of Y's age.
(x - 15) = 3/4 ⋅ (y - 15)
4(x - 15) = 3(y - 15)
4x - 60 = 3y - 45
4x = 3y + 15 ----(2)
Solving (1) and (2), we get
x = 36 years
y = 43 years
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and Venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6
©All rights reserved. onlinemath4all.com
Recent Articles
-
Linear Growth and Decay
May 22, 22 03:05 AM
Linear Growth and Decay
-
Worksheet on Probability
May 22, 22 01:15 AM
Worksheet on Probability
-
Probability Worksheet
May 22, 22 01:12 AM
Probability Worksheet