Jon is 5 years older than Dana. Ella is twice as old as Jon and Zach is twice as old as Dana. The sum of their ages is 93. How old is Jon?

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25-09-2020
Mathematics

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Jon is 5 years older than Dana. Ella is twice as old as Jon and Zach is twice as old as Dana. The sum of their ages is 93. How old is Jon?

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adioabiola adioabiola · Answer 1 · 2020-10-01T02:15:50+02:00

Answer:

Dana's age = 13 years

Zach's age = 26 years

Jon's age= 18 years

Ella's age = 36 years

Step-by-step explanation:

Let

Dana's age = x

Zach's age = 2x

Jon's age= x + 5

Ella's age = 2(x + 5)

Sum of their age = 93

x + 2x + (x + 5) + 2(x + 5) = 93

x + 2x + x + 5 + 2x + 10 = 93

6x + 15 = 93

Subtract 15 from both sides

6x + 15 - 15 = 93 - 15

6x = 78

Divide both sides by 6

x = 78/6

= 13

Therefore,

Dana's age = x = 13 years

Zach's age = 2x

= 2(13)

= 26 years

Jon's age= x + 5

= 13 + 5

= 18 years

Ella's age = 2(x + 5)

= 2(13+5)

= 26+10

= 36 years

Dana's age = 13 years

Zach's age = 26 years

Jon's age= 18 years

Ella's age = 36 years

Sum of their age = 13 + 26 + 18 + 36

= 93 years