Maths-
General
Easy
Question
If 2w + 4t = 14 and 4w + 5t = 25, what is the value of 2w + 3t ?
- 6
- 10
- 13
- 17
The correct answer is: 13
○ The concept used in the question is the concept of the solving linear equation.
○ Given equations are linear equations in two variables.
○ Methods of Solving Linear Equations.
- Graphical Method
- Elimination Method
- Substitution Method
- Cross Multiplication Method
- Matrix Method
- Determinants Method
○ In the elimination method, any of the coefficients is first equated and eliminated. After elimination, the equations are solved to obtain the other equation.
- Step by step explanation:
○ Given:
2w + 4t = 14
4w + 5t = 25
○ Step 1:
○ Let,
2w + 4t = 14 —------ eq.1
4w + 5t = 25 —---------eq.2
○ Step 2:
○ Now equate coefficient of w
∴ multiply equation 1 by 2
[ 2w + 4t = 14 ] 2
4w + 8t = 28 —---- eq.3
○ Step 3:
○ Now subtract equation eq. 2 from eq.3
4w + 8t = 28
-4w - 5t = -25
—--------------------
3t = 3
t = 1
○ Step 4:
○ Put t = 1 in equation 2
4w + 5t = 25
4w + 5 = 25
4w = 25 - 5
4w = 20
w = 
w = 5
∴ (w, t) = ( 5, 1 )
○ Step 3:
○ Put value of w and t in 2w + 3t
2w + 3t = 2.(5) + 3(1)
10 + 3
13
- Final Answer:
Hence, the value 2w + 3t is 13.
Related Questions to study
Maths-
The total cost to make one batch of soup is . What is the approximate cost per calorie, in cents?
The total cost to make one batch of soup is . What is the approximate cost per calorie, in cents?
Maths-General
Maths-
The nutrition information for a chicken noodle soup recipe is shown in the table. One batch of soup consists of 6 servings. ( 1 serving cup)
Approximately how many calories from fat are in one serving of the soup?
The nutrition information for a chicken noodle soup recipe is shown in the table. One batch of soup consists of 6 servings. ( 1 serving cup)
Approximately how many calories from fat are in one serving of the soup?
Maths-General
Maths-
Water quality managers estimate that a population of algae initially covered square miles of water in a nearby river. After a period of time, the algae grew to cover of its original area. Which of the following expressions represents the area of water, in square miles, that the algae covered after this period of time?
Water quality managers estimate that a population of algae initially covered square miles of water in a nearby river. After a period of time, the algae grew to cover of its original area. Which of the following expressions represents the area of water, in square miles, that the algae covered after this period of time?
Maths-General
Maths-
Which of the following graphs could represent the relationship between the number of manuscripts, , and the cost, , of acquiring ISBNs for the manuscripts?
Which of the following graphs could represent the relationship between the number of manuscripts, , and the cost, , of acquiring ISBNs for the manuscripts?
Maths-General
Maths-
Costs of some steps to publish a manuscript can vary, as shown in the table.
Ewan writes 30 manuscripts and wants to get them published. What is the minimum cost, in dollars, for professional review of Ewan's manuscripts?
Costs of some steps to publish a manuscript can vary, as shown in the table.
Ewan writes 30 manuscripts and wants to get them published. What is the minimum cost, in dollars, for professional review of Ewan's manuscripts?
Maths-General
Maths-
What is the solution to the given equation?
What is the solution to the given equation?
Maths-General
Maths-
The scatterplot shows the average price per square foot of a house in the United States each year for several years. A line of best fit for the data is also shown.
The line of best fit predicted that the average price per square foot in 2001 would be . What is the difference between the predicted value and the actual average price per square foot in 2001 ?
The scatterplot shows the average price per square foot of a house in the United States each year for several years. A line of best fit for the data is also shown.
The line of best fit predicted that the average price per square foot in 2001 would be . What is the difference between the predicted value and the actual average price per square foot in 2001 ?
Maths-General
Maths-
In the given equation, k is a constant. The equation has no solution. What is the value of k?
An inconsistent system is a set of equations for which no solution exists.
One solution of the system is shown as x = y = z = 0. D must be zero for endless solutions (including non-zero ones). There are thus two possible possibilities for k, but there is only one non-zero answer, e.g.: The value of K can be 2 or 0.5.
In the given equation, k is a constant. The equation has no solution. What is the value of k?
Maths-General
An inconsistent system is a set of equations for which no solution exists.
One solution of the system is shown as x = y = z = 0. D must be zero for endless solutions (including non-zero ones). There are thus two possible possibilities for k, but there is only one non-zero answer, e.g.: The value of K can be 2 or 0.5.
Maths-
4x + y = 7
2x - 7y = 1
If(x, y) is the solution to the given system of equations, what is the value of x ?
4x + y = 7
2x - 7y = 1
If(x, y) is the solution to the given system of equations, what is the value of x ?
Maths-General
Maths-
The graph of 
where a and c are constants, is shown. What is the value of a ?
The graph of where a and c are constants, is shown. What is the value of a ?
Maths-General
Maths-
x2 - 2x – 1 = 0
The equation above has solutions 
and 
where n and k are positive integers. What is the value of n + k ?
x2 - 2x – 1 = 0
The equation above has solutions and where n and k are positive integers. What is the value of n + k ?
Maths-General
Maths-
An office building has a room with a square-shaped floor. The actual length of the floor is 90 times the length of the floor on a blueprint drawn to scale. The actual area of the floor is p times the area of the floor on the blueprint. What is the value of p ?
An office building has a room with a square-shaped floor. The actual length of the floor is 90 times the length of the floor on a blueprint drawn to scale. The actual area of the floor is p times the area of the floor on the blueprint. What is the value of p ?
Maths-General
Maths-
In the figure shown, BC is parallel to AD and AB =CD . What is the perimeter of quadrilateral ABCD?
In the figure shown, BC is parallel to AD and AB =CD . What is the perimeter of quadrilateral ABCD?
Maths-General
General
A manager purchased cones for ice cream. Find a formula for the length of the radius , in terms of its volume V.
For such questions, we should know the formula of cone.
A manager purchased cones for ice cream. Find a formula for the length of the radius , in terms of its volume V.
GeneralGeneral
For such questions, we should know the formula of cone.
Maths-
The function 
is defined by 
For what value of x does 
?
The function is defined by For what value of x does ?
Maths-General
