**11. Correct answer: 8, 10 or 12**

Given:

When the positive even integer *n* is increased by 50% of itself, the result is between 10 and 20:

To find:

One possible value of *n *

Solution:

Topic(s): Percent

10 < *n* + 50%*n * < 20

10 < *n* + 0.5*n* < 20

10 < 1.5*n* < 20

6.67 < *n* < 13.33

Remember, *n* is an even integer.

The possible even integers in the required range, 6.67 < *n* < 13.33, would be 8, 10 and 12

**Answer: Any one of following: 8, 10 or 12**

**12. Correct answer: 3400**

Given:

The perimeter of the rectangle is 250.

The length of one side is 40.

To find:

Area of the rectangle

Solution:

Topic(s): Area and perimeter of rectangle

First, we need to find the length of the other side of the rectangle.

Formula of perimeter of rectangle: 2(*l* + *w*)

Substitute in the given values:

2(40 + *w*) = 250

80 + 2*w* = 250

2*w* = 170

*w* = 85

Next, we calculate the area

Formula for area of rectangle: *lw
*

**Answer: 3400**

**13. Correct answer: 450**

Given:

A school ordered $600 worth of light bulbs

Some bulbs cost $1 each

Some bulbs cost $2 each

There are twice as many $1 bulbs as $2 bulbs

To find:

The number of light bulbs ordered altogether

Solution:

Topic(s): Integer word problem

Let *b* be the number of $2 light bulbs ordered

2*b* be the number of $1 light bulbs ordered

Altogether, the school ordered $600 worth of light bulbs.

*b *× 2 + 2*b* × 1 = 600

2*b* + 2*b* = 600

4*b* = 600

*b* = 150

Total number of bulbs = *b* + 2*b* = 3*b* = 3 × 150 = 450

**Answer: 450**

**14. Correct answer: 1/2**

Given:

4(*x* + *y*)(*x* – *y*) = 40 (equation 1)

*x* – *y *= 20 (equation 2)

To find:

*x* + *y*.

Solution:

Topic(s): Substitution

Substitute equation 2 into equation 1

4(*x* + *y*) × 20 = 40

4(*x* + *y*) = 2

(*x* + *y*) =

**Answer: **

**15. Correct answer: 12**

Given:

The center of the circle has coordinates (5, 12)

The circle touches the *x*-axis at one point only.

To find:

The radius of the circle.

Solution:

Topic(s): Tangent of circle

First, we can sketch the diagram.

For the circle to touch the *x*-axis at only one point, the *x*-axis must be a tangent to the circle. A tangent is perpendicular to the radius at the point of contact. So the radius must be 12

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.