Answer:
1) [tex]n = 84[/tex]
2) [tex]n = 78[/tex]
3) [tex]n = 24[/tex]
4) [tex]n = 16[/tex]
5) [tex]n = 35[/tex]
Step-by-step explanation:
To solve each proportion, we apply cross multiplication.
Question 1:
[tex]\frac{5}{12} = \frac{35}{n}[/tex]
[tex]5n = 35*12[/tex]
Simplifying both sides by 5
[tex]n = 7*12 = 84[/tex]
Question 2:
[tex]\frac{n}{52} = \frac{180}{120}[/tex]
[tex]120n = 52*180[/tex]
Simplifying both sides by 20
[tex]6n = 52*9[/tex]
Simplifying by 3
[tex]2n = 52*3[/tex]
Simplifying by 2
[tex]n = 26*3 = 78[/tex]
Question 3:
[tex]\frac{18}{n} = \frac{21}{28}[/tex]
[tex]21n = 18*28[/tex]
Simplifying both sides by 7
[tex]3n = 18*4[/tex]
Simplifying both sides by 3
[tex]n = 6*4 = 24[/tex]
Question 4:
[tex]\frac{n}{4} = \frac{24}{6}[/tex]
[tex]\frac{n}{4} = 4[/tex]
[tex]n = 16[/tex]
Question 5:
[tex]\frac{10}{16} = \frac{n}{56}[/tex]
[tex]16n = 56*10[/tex]
Simplifying by 2, both sides
[tex]8n = 56*5[/tex]
Simplifying by 8, both sides
[tex]n = 7*5 = 35[/tex]
The given expressions can be evaluated by using the arithmetic operations in order to find the value of 'n' in each case.
1) 5/12 = 35/n
Cross multiply in the above expression.
5n = 35 [tex]\times[/tex] 12
Further, simplify the above expression.
n = 84
2) n/52 = 180/120
Cross multiply in the above expression.
180n = 120 [tex]\times[/tex] 52
180n = 6240
Divide 180 by 6240 in the above expression.
n = 34.67
3) 18/n = 21/28
Cross multiply in the above expression.
18 [tex]\times[/tex] 28 = 21n
504 = 21n
Divide 504 by 21 in the above expression.
n = 24
4) n/4 = 24/6
Cross multiply in the above expression.
6n = 24 [tex]\times[/tex] 4
6n = 96
Divide 96 by 6 in the above expression.
n = 16
5) 10/16 = n/56
Cross multiply in the above expression.
10 [tex]\times[/tex] 56 = 16n
560 = 16n
Divide 560 by 16 in the above expression.
n = 35
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