Question

Maddy's age is twice that of Champ's. The ratio of Bill's and Champ's
ages is 2:3. What is the age of the oldest person, given that the sum
of the ages of Bill, Champ and Maddy is 88 years?​

Answer 1

Answer :-

• The oldest person is Maddy.
• His age is 48 years.

Given :

• Maddy's age is twice that of Champ's.

• The ratio of Bill's and Champ's age is 2 : 3.

• The sum of the ages of Bill, Champ and Maddy is 88 years.

To find :-

• The age of the oldest person.

Step-by-step explanation :-

• The ratio of Bill's and Champ's ages is 2 : 3. So let their ages be 2x and 3x respectively.

• It has been given that Maddy's age is twice that of Champ's age. Here, Champ's age is 3x, so Maddy's age will be 3x × 2 = 6x.

• Now, it has been given that the sum of the ages of Bill, Champ and Maddy is 88 years. So, that means the sum of 2x, 3x and 6x is 88.

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$\longmapsto\sf2x + 3x + 6x = 88$

Adding 2x, 3x and 6x,

$\longmapsto\sf11x = 88$

Transposing 11 from LHS to RHS, changing it's sign,

$\longmapsto\sf x = \dfrac{88}{11}$

Dividing 88 by 11,

$\longmapsto\overline{\boxed{ \sf x = 8}}$

• The value of x is 8.

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Now let's find their ages!

$\Rightarrow\bf Bill's \: age =2x = 2 \times 8 = 16.$

$\Rightarrow\bf Champ's \: age =3x = 3 \times 8 = 24.$

$\Rightarrow\bf Maddy's \: age = 6x = 6 \times 8 = 48.$

It's clear that :-

$\underline{\overline{\boxed{\rm48 \: is \: the \: greatest \: number \: here.}}}$

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• Hence, Maddy is the oldest person and his age is 48 years.