Advertisements
Advertisements
Question
Solve for x and y:
0.3x + 0.5y = 0.5, 0.5x + 0.7y = 0.74
Solution
The given system of equations is
0.3x + 0.5y = 0.5 …….(i)
0.5x + 0.7y = 0.74 …….(ii)
Multiplying (i) by 5 and (ii) by 3 and subtracting (ii) from (i), we get
2.5y - 2.1y = 2.5 - 2.2
⇒0.4y = 0.28
⇒y = `(0.28)/(0.4)` = 0.7
Now, substituting y = 0.7 in (i), we have
0.3x + 0.5 × 0.7 = 0.5
⇒0.3x = 0.50 – 0.35 = 0.15
⇒x =` (0.15)/(0.3)` = 0.5
Hence, x = 0.5 and y = 0.7.
APPEARS IN
RELATED QUESTIONS
In the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:
3x - 5y = 20
6x - 10y = 40
For what value of α, the system of equations
αx + 3y = α - 3
12x + αy = α
will have no solution?
Solve for x and y:
217x + 131y = 913, 131x + 217y = 827
Solve for x and y:
`ax - by = a^2 + b^2, x + y = 2a`
A chemist has one solution containing 50% acid and a second one containing 25% acid. How much of each should be used to make 10 litres of a 40% acid solution?
In a cyclic quadrilateral ABCD, it is given ∠A = (2x + 4)°, ∠B = (y + 3)°, ∠C = (2y + 10)° and ∠D = (4x – 5)°. Find the four angles.
Find the values of k for which the system of equations 3x + ky = 0,
2x – y = 0 has a unique solution.
Find the value of k for which the system of equations kx – y = 2 and 6x – 2y = 3 has a unique solution.
The pair of equations x = a and y = b graphically represents lines which are ______.
Read the following passage:
|
A coaching institute of Mathematics conducts classes in two batches I and II and fees for rich and poor children are different. In batch I, there are 20 poor and 5 rich children, whereas in batch II, there are 5 poor and 25 rich children. The total monthly collection of fees from batch I is ₹9,000 and from batch II is ₹26,000. Assume that each poor child pays ₹x per month and each rich child pays ₹y per month.
|
Based on the above information, answer the following questions:
- Represent the information given above in terms of x and y.
- Find the monthly fee paid by a poor child.
OR
Find the difference in the monthly fee paid by a poor child and a rich child. - If there are 10 poor and 20 rich children in batch II, what is the total monthly collection of fees from batch II?
