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

SABIW

wrong tanan imong answer

Thank you for sharing this. I just want to ask if you have a copy of the Grade 7 MTAP division orals? thank you 🙂

last 2014-2015., and 2015-2016, thanks 🙂

I don’t have. If you can give me a copy, I will solve and post the solutions.

can help me search for division oral 2015.

good day please answer.. cora multiplies a number by 2 instead of squaring it. then she subtracted 9 from the result instead of dividing the result by 9. if the result of the wrong calculation is 3, what is the result of the correct calculation?

a group of children arranged themselves into circle. from remy and counting clockwise, nita is the 8th child. from remy and counting counter clockwise, nita is 15th child. how many children are there in all?