Mathematics Questions

A two-digit number is such that the sum of its digits is 9. If the digits are interchanged, the number increases by 9. Find the number.

The cost of 2 pencils and 3 pens is Rs 40. The cost of 3 pencils and 2 pens is Rs 35. Find the cost of a pencil.

Solve for x: x/2 + x/3 + x/4 = 13.

What value of a makes the lines ax + 2y = 5 and 2x + y = 3 parallel?

Solve for y: 4/(y-1) = 2.

If x/y = 2/3 and x + y = 10, find x.

Find the x-intercept of the line 3x - 4y = 12.

Solve: 2x - (x - 3) = 5.

The difference of two numbers is 10 and their ratio is 3:2. Find the smaller number.

For what value of k will the system 2x + 3y = 7 and 4x + ky = 14 have infinitely many solutions?

The sum of a number and its reciprocal is 2. (This results in a linear form if simplified). Find the number.

Solve: 15/x = 5/2.

If 2x + y = 7 and x + 2y = 8, find the value of x - y.

A taxi charge consists of a fixed fee plus a charge per km. If for 10 km the charge is Rs 150 and for 15 km it is Rs 200, find the fixed fee.

Solve for x: (2x+1)/3 + 1 = x.

Find the value of k for which the system of equations has no solution.

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Find the speed of the boat in still water.

Solve the following literal equation for x.

If 2/x + 3/y = 13 and 5/x - 4/y = -2, find x.

Five years ago, a father's age was 7 times his son's age. Five years hence, the father's age will be 3 times his son's age. Find the father's present age.