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Answer:
1.96. 6.22:33:55
2.10. 7. 4
3.44:77 8.1500
4.12. 9.24
5.375. 10.144
Step-by-step explanation:
1.Since 10 : 16 = 60 : X
Then we know
16/10 = X/60
Multiplying both sides by 60 cancels on the right
60 × (16/10) = (X/60) × 60
60 × (16/10) = X
Then solving for X
X = 60 × (16/10)
X = 96
Therefore
10 : 16 = 60 : 96
2.Since6 : X = 72 : 120
Then we know
X/6 = 120/72
Multiplying both sides by 6 cancels on the left
6 × (X/6) = (120/72) × 6
X = (120/72) × 6
Then solving for X
X = 6 × (120/72)
X = 10
Therefore
6 : 10 = 72 : 120
3.Divide 121 into two parts in the ratio 4 : 7
Since, 4 + 7= 11.
Therefore, first part = 4/11 × 121 = 44
Second part = 7/11 × 121 = 77
4.Cross multiply:
20 * X = 10 * 24
Simplifying
20 * X = 10 * 24
Multiply 10 * 24
20X = 240
Solving
20X = 240
Solving for variable 'X'.
Move all terms containing X to the left, all other terms to the right.
Divide each side by '20'.
X = 12
5.Cross multiply:
450 * 25 = U * 30
Simplifying
450 * 25 = U * 30
Multiply 450 * 25
11250 = U * 30
Reorder the terms for easier multiplication:
11250 = 30U
Solving
11250 = 30U
Solving for variable 'U'.
Move all terms containing U to the left, all other terms to the right.
Add '-30U' to each side of the equation.
11250 + -30U = 30U + -30U
Combine like terms: 30U + -30U = 0
11250 + -30U = 0
Add '-11250' to each side of the equation.
11250 + -11250 + -30U = 0 + -11250
Combine like terms: 11250 + -11250 = 0
0 + -30U = 0 + -11250
-30U = 0 + -11250
Combine like terms: 0 + -11250 = -11250
-30U = -11250
Divide each side by '-30'.
U = 375
6.Divide 110 into three parts in the ratio 2 :3 :5
Since, 2+3+5= 10
Therefore, first part = 2/10 × 110= 22
Second part = 3/10 × 110= 33
Third part =5/10 × 110= 55
Therefore the terms of 110 are 22:33:55
7.Simplifying X * 40 = 16 * 10
Reorder the terms for easier multiplication:
40X = 16 * 10
Multiply 16 * 10
40X = 160
Solving
40X = 160
Solving for variable 'X'.
Move all terms containing X to the left, all other terms to the right.
Divide each side by '40'.
X = 4
8.Cross multiply:
900 * 50 = U * 30
Simplifying
900 * 50 = U * 30
Multiply 900 * 50
45000 = U * 30
Reorder the terms for easier multiplication:
45000 = 30U
Solving
45000 = 30U
Solving for variable 'U'.
Move all terms containing U to the left, all other terms to the right.
Add '-30U' to each side of the equation.
45000 + -30U = 30U + -30U
Combine like terms: 30U + -30U = 0
45000 + -30U = 0
Add '-45000' to each side of the equation.
45000 + -45000 + -30U = 0 + -45000
Combine like terms: 45000 + -45000 = 0
0 + -30U = 0 + -45000
-30U = 0 + -45000
Combine like terms: 0 + -45000 = -45000
-30U = -45000
Divide each side by '-30'.
U = 1500
9.Let n = one number
then
(84-n) = the other the other number
n = 2
84-n. 5
Cross multipoly
5n = 2(84-n)
5n = 168 - 2n
5n + 2n = 168
n = 168/7
n = 24 is the smaller number
10.Divide 480 into three parts in the ratio 2 :3 :5
Since, 2+3+5= 10
Therefore, first part = 2/10 × 480= 96
Second part = 3/10 × 480= 144
Third part =5/10 × 480= 240
Therefore the middle terms is 144
hope it helps you! Stay safe and goodluck on your studies!