Q11: 31 and 44
Q12: -5, 15, -9, 19
Q13: 16
Step-by-step explanation:
Question 10
Let x = smaller part
Let y = larger part
Given sum of parts is 75:
x + y = 75
Given the larger part is 13 more than the smaller part:
y = 13 + x
Substitute y = 13 + x into x + y = 75 and solve for x:
⇒ x + 13 + x = 75
⇒ 2x + 13 = 75
⇒ 2x = 62
⇒ x = 31
Substitute found value of x into y = 13 + x and solve for y:
⇒ y = 13 + 31
⇒ y = 44
Therefore, the smaller part is 31 and the larger part is 44
Question 11
Let x = first number
Let y = second number
Let z = third number
Let w = fourth number
Given the first is 20 less than the second:
x = y - 20
⇒ y = x + 20
Given the third is 1 more than twice the first:
z = 2x + 1
Given the fourth is 4 more than the second:
w = y + 4
Given the sum of the first and second equals the sum of the third and fourth numbers:
x + y = z + w
Substitute the first 3 equations into x + y = z + w and rearrange to make y the subject:
⇒ (y - 20) + y = (2x + 1) + (y + 4)
⇒ 2y - 20 = 2x + y + 5
⇒ y = 2x + 25
Rearrange x = y - 20 to make y the subject:
x = y - 20
⇒ y = x + 20
Now equate the equations and solve for x:
⇒ x + 25 = 20
⇒ x = -5
Now we have found the value of x, substitute into z = 2x + 1 to find z:
⇒ z = 2(-5)+ 1
⇒ z = -9
and substitute the value of x into y = x + 20 to find y:
⇒ y = -5 + 20
⇒ y = 15
finally substitute the value of y into w = y + 4 to find w:
⇒ w = 15 + 4
⇒ w = 19
Therefore,
first number = -5second number = 15third number = -9fourth number = 19Question 12
Let x = unknown number
Given one quarter of a number is being increased by one half of the same number is 12: