Question

The sum of bob mary and joe’s ages is 85. bob is 15 less than joe. Mary is twice joe. How old is Mary

Answer 1

Let Joe's age be x

Let Bob's age be x-15

Let Mary's age be 2x

Now,

`\mathcal{Bob's \: age+ Joe's \: age+ Mary's \: age = 85}`

Substitute the values we just gave ATQ

`\sf \: x - 15 + x + 2x = 85 \\ \sf \: 4x - 15 = 85 \\ \sf \: 4x = 85 + 15 \\ \sf \: 4x = 100 \\ \sf \: x = 25`

Find their ages with the help of value of x we just found!~

`\large{|\underline{\mathtt{\red{b}\blue{o}\orange{b}\pink{'}\blue{ s }\purple{ \: }\green{a}\red{g}\blue{e}\purple{ \searrow}}}}`

`\tt \: x - 15 \\ \tt \: 25 - 15 \\ \colorbox{lightyellow}{\bf \: = 10}`

`\large{|\underline{\mathtt{\red{j}\blue{o}\orange{e}\pink{'}\blue{ s }\purple{ \: }\green{a}\red{g}\blue{e}\purple{ \searrow}}}}`

`\tt \: x \\ \colorbox{lightyellow}{\bf \: = 25}`

`\large{|\underline{\mathtt{\red{m}\blue{a}\orange{r} \green{y}\pink{'}\blue{ s }\purple{ \: }\green{a}\red{g}\blue{e}\purple{ \searrow}}}}`

`\tt \: 2x \\ \tt \: 2 * 25 \\ \colorbox{lightyellow}{\bf \: = 50}`

Therefore,

• Bob's age = 10
• Joe's age = 25
• Mary's age = 50

Answer 2

Joe's age = 25 years

Mary's age = 50 years

Bob's age = 10 years

Explanation:

Joe's age = x years

Mary's age = 2*x = 2x

Bob's age = x - 15

Sum of their ages = 85

x + 2x + x - 15 = 85

Combine like terms,

4x - 15 = 85

Add 15 to both sides

4x - 15 + 15 = 85 + 15

4x = 100

Divide both sides by 4

x = 100/4

x = 25

Joe's age = 25 years

Mary's age = 2*25 = 50 years

Bob's age = 25 - 15 = 10 years