Question
A housewife finds that 5 cans of condensed milk and 3 jars of instant coffee cost Rs 27 while 12 cans of condensed milk and 5 jars of instant coffee cost Rs.49. Find the total cost for 7 cans of condensed milk and 2 jars of instant coffee.
Hint:
- Hint:
○ Form the equation according to given information..
○ Take variable values as x or any alphabet.
○ Solve the equation to get value of x.
○ The concept used in the question is the concept of solving linear equations.
○ 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.
The correct answer is: x + y = 4
- Step by step explanation:
○ Given:
5 cans of condensed milk and 3 jars of instant coffee cost Rs 27
12 cans of condensed milk and 5 jars of instant coffee cost Rs.49.
○ Step 1:
○ Let, cost of can of condensed milk be x and cost of jar of instant coffee be y.
so,
According to given information:
5x + 3y = 27 and
12x + 5y = 49
○ Step 2:
5x + 3y = 27
12x + 5y = 49
○ Let,
5x + 3y = 27 —------ eq.1
12x + 5y = 49 —---------eq.2
○ Step 2:
○ Now equate coefficient of y
∴ multiply equation 1 by 5 and multiply equation 2 by 3
[5x + 3y = 27 ] 5
25x + 15y = 135 —---- eq.3
[12x + 5y = 49 ] 3
36x + 15y = 147 —---- eq.4
○ Step 3:
○ Now subtract equation eq. 3 from eq.4
36x + 15y = 147
- 25x - 15y = - 135
—--------------------
11x = 12
∴ x =
○ Step 4:
○ Put x = in equation 1
5x + 3y = 27
5( ) + 3y = 27
3y = 27 -
3y =
y =
y =
Therefore,
x + y = 4 + 0
x + y = 4
- Final Answer:
Correct option is
Option C. 4.
○ Step 2:
○ Now equate coefficient of y
∴ multiply equation 1 by 5 and multiply equation 2 by 3
○ Step 3:
○ Now subtract equation eq. 3 from eq.4
∴ x =
○ Step 4:
○ Put x = in equation 1
y =
Therefore,
x + y = 4 + 0
x + y = 4
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Use inductive reasoning to make a conjecture about the sum of a number and itself. Then use deductive reasoning to show the conjecture is true.
Informally, a hypothesis is just drawing assumptions about something based on what you already know and have observed.
A conjecture is formally defined as a based-on-observations, a statement considered true.
Speculation is similar to your opinion about something you follow or perhaps a knowledgeable estimate.
For example, observe the numbers below: 2, 4, 6, 8, 10, and 12. What number would come next? You're probably thinking 14, but What led you to that conclusion, and why? You may have seen the pattern and that the list is counting in twos.
The following number is 14 because the list counts by 2's, according to your hypothesis.
You saw the pattern and concluded without making any claim.
Use inductive reasoning to make a conjecture about the sum of a number and itself. Then use deductive reasoning to show the conjecture is true.
Informally, a hypothesis is just drawing assumptions about something based on what you already know and have observed.
A conjecture is formally defined as a based-on-observations, a statement considered true.
Speculation is similar to your opinion about something you follow or perhaps a knowledgeable estimate.
For example, observe the numbers below: 2, 4, 6, 8, 10, and 12. What number would come next? You're probably thinking 14, but What led you to that conclusion, and why? You may have seen the pattern and that the list is counting in twos.
The following number is 14 because the list counts by 2's, according to your hypothesis.
You saw the pattern and concluded without making any claim.