A. Solve the following word problems
1. The ratio of boys to girls in grade 5 is 2 : 3.
a. If there are 24 boys, how many girls are there?
b. If there are 80 students, how many are girls?
c. If there are 80 students, how many more girls are there than boys?
2. There were 35 children and 10 adults at a carnival.
a. What is the ratio of adults to children at the carnival?
b. What is the ratio of children to total people at the carnival?
c. Five more children came to the carnival. Now, what is the ratio of children to total people?
3. The ratio of the number of the people outside a theatre to the number of people inside the theatre is 2 : 3. If the total number of seats in the theatre is 150, find the number of people who cannot enter the theatre because the tickets are not available.
4.The ratio of the length of a vertical pole and its
shadow on the ground is 8 : 5. Find the length of the shadow if the length of the pole is 40 m.
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ANSWER
We know that
(x
2
+y
2
+z
2
+2xy+2yz+zx)=(x+y+z)
2
(i) 4x
2
+9y
2
+16z
2
+12xy−24yz−16xz
=(2x)
2
+(3y)
2
+(−4z)
2
+2(2x)(3y)+2(3y)(−4z)+2(−4z)(2x)
=(2x+3y−4z)
2
=(2x+3y−4z)(2x+3y−4z)
(ii) 2x
2
+y
2
+8z
2
−2
2
xy+4
2
yz−8zx
=(−
2
x)+(y)
2
+(
2
z)+2(−
2
x)(y)+2(y)(2
2
z)+2(2
2
z)(y)
=(−
2
x+y+2
2
z)
2
=(−
2
x+y+2
2
z)(−
2
x+y+2
2
z)
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