Advertisements
Advertisements
Question
John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.
Advertisements
Solution
Let the number of John's marbles be x.
Therefore, number of Jivanti's marble = 45 - x
After losing 5 marbles,
Number of John's marbles = x - 5
Number of Jivanti's marbles = 45 - x - 5 = 40 - x
It is given that the product of their marbles is 124.
∴ (x - 5)(40 - x) = 124
⇒ x2 – 45x + 324 = 0
⇒ x2 – 36x - 9x + 324 = 0
⇒ x(x - 36) -9(x - 36) = 0
⇒ (x - 36)(x - 9) = 0
Either x - 36 = 0 or x - 9 = 0
⇒ x = 36 or x = 9
If the number of John's marbles = 36, Then, number of Jivanti's marbles = 45 - 36 = 9
If number of John's marbles = 9, Then, number of Jivanti's marbles = 45 - 9 = 36
APPEARS IN
RELATED QUESTIONS
Solve for x
:`1/((x-1)(x-2))+1/((x-2)(x-3))=2/3` , x ≠ 1,2,3
Solve the following quadratic equations by factorization:
`(2x)/(x-4)+(2x-5)/(x-3)=25/3`
Solve the following quadratic equations by factorization:
`3x^2-2sqrt6x+2=0`
The perimeter of a rectangular field is 82 m and its area is 400 m2. Find the breadth of the rectangle.
Solve each of the following equations by factorization:
x(x – 5) = 24
Divide 57 into two parts whose product is 680.
If \[1 + \sqrt{2}\] is a root of a quadratic equation will rational coefficients, write its other root.
If x = 1 is a common root of ax2 + ax + 2 = 0 and x2 + x + b = 0, then, ab =
Solve the following equation: 4x2 + 16x = 0
Solve the following equation: `"a"/("x" - "a") + "b"/("x" - "b") = (2"c")/("x" - "c")`
The sum of the square of 2 positive integers is 208. If the square of larger number is 18 times the smaller number, find the numbers.
The speed of an express train is x km/hr arid the speed of an ordinary train is 12 km/hr less than that of the express train. If the ordinary train takes one hour longer than the express train to cover a distance of 240 km, find the speed of the express train.
Solve the following quadratic equation by factorisation:
9x2 - 3x - 2 = 0
In each of the following, determine whether the given values are solution of the given equation or not:
`x = 1/x = (13)/(6), x = (5)/(6), x = (4)/(3)`
In each of the following, determine whether the given values are solution of the given equation or not:
`a^2x^2 - 3abx + 2b^2 = 0; x = a/b, x = b/a`.
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
The hotel bill for a number of people for an overnight stay is Rs. 4800. If there were 4 more, the bill each person had to pay would have reduced by Rs. 200. Find the number of people staying overnight.
Complete the following activity to solve the given quadratic equation by factorization method.
Activity: x2 + 8x – 20 = 0
x2 + ( __ ) – 2x – 20 = 0
x (x + 10) – ( __ ) (x + 10) = 0
(x + 10) ( ____ ) = 0
x = ___ or x = 2
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
Find the roots of the quadratic equation x2 – x – 2 = 0.
