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 + .05x= 25, 000
0.05x = 15, 000
x = 300 000
Answer: Php 300, 000.00
44.) What is the absolute value of 
Solution
Answer:
45.) Find all real numbers for which (7 – x)/2 > (4x + 3)/4
Solution
Multiplying both sides by 4, we have
2(7 – x) > 4x + 3
14 – 2x > 4x + 3
11 > 6x
11/6 > x
x < 11/6
46.) For what values of x is (3x – 1)/4 < (2x + 5)/3?
Solution
Multiplying both sides by 12, we obtain
3(3x – 1) < 4(2x + 5)
9x – 3 < 8x + 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: 7x – 3y = 23 and x + 2y = 13.
Solution
Multiplying x + 2y = 13 by -7, we have
-7x – 14y = -91 (*)
7x – 3y = 23 (**)
Adding (*) and (**), we obtain
-17y = -68
y = 4.
Substituting y to x + 2y = 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 + 4x
3x = 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