This is the fifth part of the Metrobank-MTAP Math Challenge Questions for Grade 7. In this post, we discuss the solutions to number 41-50. You can also read the solutions to **1-10**, **11-20**, **21 – 30**, and **31-40**.

**41.)** Each square in the figure has side length 1. The curve each square is a circular arc with center at a corner of the square. What is the area of the shaded region?

Solution: will be discussed in a separate post.

**Answer:** 8 square units

**42.)** What is the least common multiple of 168 and 420?

**Solution**

Left as an exercise.

**Answer:** 840

**43.)** A salesman receives a basic salary of Php10, 000 and a commission of 5% on all sales. Find his total sales in a month when he earned Php25, 000?

**Solution**

10, 000 + .05*x*= 25, 000

0.05*x *= 15, 000

*x* = 300 000

**Answer:** Php 300, 000.00

**44.)** What is the absolute value of at ?

**Solution**

**Answer:**

**45.)** Find all real numbers for which (7 – *x*)/2 > (4*x* + 3)/4

**Solution**

Multiplying both sides by 4, we have

2(7 – *x*) > 4*x* + 3

14 – 2*x* > 4*x* + 3

11 > 6*x*

11/6 >* x*

*x* < 11/6

46.) For what values of *x* is (3*x* – 1)/4 < (2*x* + 5)/3?

**Solution**

Multiplying both sides by 12, we obtain

3(3*x* – 1) < 4(2*x* + 5)

9*x* – 3 < 8*x* + 20

*x* < 23

**47.)** Write an equation of the line through (-2, 3) and (1,4).

Solution

The slope of the line is m = (4 – 3)/(1-(-2)) = 1/3.

We use the point slope form. That is,

y – 4 = (1/3)(x – 1)

y – 4 = 1/3x – 1/3

3y = x + 11

y = (x + 11)/3

Answer: y = (x + 11)/3

**48.)** Solve for *x* and *y*: 7*x* – 3*y* = 23 and *x* + 2*y* = 13.

**Solution**

Multiplying *x* + 2*y* = 13 by -7, we have

-7*x* – 14*y* = -91 (*)

7*x* – 3*y* = 23 (**)

Adding (*) and (**), we obtain

-17*y* = -68

*y* = 4.

Substituting *y* to *x* + 2*y* = 13,

*x *+ 2(4) = 13

*x* = 5

**49.)** Pete is 12 years old and His grandfather 63 years old. And how many years we’ll be age be one fourth of his grandfather?

**Solution **

Let* x* be the number of years to be added to both ages.

(1/4)(63 + *x*) = 12 + *x*

Multiplying both sides by 4,

63 + *x* = 48 + 4*x*

3*x* = 15

*x* = 5

Answer: 5 years

**50.)** ABC has its coordinates at A(*a*, -1), B(8, -1), and C(5,4). If the base is twice the height, find *a*.

**Solution**

If we let AB be the base, then the height is the difference between y-coordinate of C and -1. That is, |4 -(-1)| = 5.

Now, *|a* – 8| = 2(5) = 10

*a* – 8 = 10

*a* = 18

-(*a* – 8) = 10

8 – *a* = 10

–*a* = 2

*a* = -2

Answers: *a* = -2 or* a* = 18