Form the equation and solve.
a. A number is 12 more than the other. Find the numbers if their sum is 48.
b. Twice the number decreased by 22 is 48. Find the number.
c. The sum of two consecutive even numbers is 38. Find the numbers.
d. Seven times the number is 36 less than 10 times the number. Find the number.
e. 4/5 of a number is more than 3/4 of the number by 5. Find the number.
f. Among the two supplementary angles, the measure of the larger angle is 36° more than
the measure of smaller. Find their measures.
g. In a class of 42 students, the number of boys is 2/5 of the girls. Find the number of boys
and girls in the class.
Answer:
a) Numbers = 18, 30
b) Number = 35
c) Numbers = 18, 29
d) Number = 12
e) Number = 100
f) Measures = 72°, 108°
g) Number of boys = 12
Number of girls = 30
Step-by-step explanation:
a) Let the number be x
Other number = x + 12
Their sum = 48
ie, x + x + 12 = 48
2x + 12 = 48
2x = 48 – 12 = 36
x = 36 ÷ 2 = 18
So, the first number = 18
Other number = 18 + 12 = 30
b) Let the number = x
Given that 2x – 22 = 48
2x = 48 + 22 = 70
x = 35
Number = x = 35
c) Let the first even number = n
Second even number = n + 2
n + n + 2 = 38
2n + 2 = 38
2n = 38 – 2 = 36
n = 36 ÷ 2 = 18
First even number = n = 18
Second even number = n + 2 = 18 + 2 = 20
d) Let the number be x
Given that, 10x – 36 = 7x
10x – 7x = 36
3x = 36
x = 36 ÷ 3 = 12
Number = x = 12
e) Let the number = x
⅘ of the number = ⅘x
¾ of the number = ¾x
Given that,
[tex] \frac{3}{4} x + 5 = \frac{4}{5} x \\ \frac{3x}{4} + 5 = \frac{4x}{5} \\ 5 = \frac{4x}{5} – \frac{3x}{4} = \frac{16x}{20} – \frac{15x}{20} \\ 5 = \frac{x}{20} \\ x = 20 \times 5 = 100[/tex]
Number = 100
f) Let the measure of the smaller angle = x
Larger angle = x + 36
Since they are supplementary angles, their sum will be 180°
ie, x + x + 36 = 180
2x + 36 = 180
2x = 180 – 36 = 144
x = 144 ÷ 2 = 72
Smaller angle = x = 72°
Larger angle = 72 + 36 = 108°
g) Let the number of girls = x
Number of boys = ⅖x
Total number of students = 42
That is,
[tex]x + \frac{2}{5} x = 42 \\ \frac{x}{1} + \frac{2x}{5} = 42 \\ \frac{5x}{5} + \frac{2x}{5} = 42 \\ \frac{7x}{5} = 42 \\ 7x = 42 \times 5 = 210 \\ x = \frac{210}{7} = 30[/tex]
Number of girls = x = 30
Number of boys = 42 – 30 = 12
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