Question

sara travels twice as far as Eli when going to camp. Ashley travels as far as Sara and Eli together. Hazel travels 3 times as far as Sara. In total , all four travel a total of 888 miles to camp. How far do each of them travel?

Answer 1

Let's represent how far Eli travels as x.
Sara travels twice as far as that, so 2x.
Ashley travels as far as Eli and Sara combined. x + 2x = 3x.
Hazel travels 3× as far as Sara, and 3×2x = 6x.

All of these add up to 888.
x + 2x + 3x + 6x = 888
Let's add up these like terms.
12x = 888
We can then divide each side by 12...
x = 74

Therefore, Eli traveled 74 miles!
We can use this value to figure out everyone else's distances as well.
Sara = 2 × 74 = 148
Ashley = 3 × 74 = 222
Hazel = 6 × 74 = 444

Answer 2

• Sara: 148 miles
• Eli: 74  miles
• Ashley: 222  miles
• Hazel: 444 miles

Further explanation

Given:

• Sara travels twice as far as Eli when going to camp.
• Ashley travels as far as Sara and Eli together.
• Hazel travels three times as far as Sara.
• In total, all four travel a total of 888 miles to camp.

Question:

How far does each of them travel?

The Process:

Notice of the four people, the easiest way is to start from Eli.

Let's call Eli's travel as x.

$\boxed{ \ Eli's \ travel = x \ }$

Sara travels twice as far as Eli.

$\boxed{ \ Sara's \ travel = 2x \ }$

Ashley travels as far as Sara and Eli together.

$\boxed{ \ Ashley's \ travel = x + 2x \rightarrow \boxed{ \ Ashley's \ travel = 3x \ }}$

Hazel travels three times as far as Sara.

$\boxed{ \ Hazel's \ travel = 3 \times 2x \rightarrow \boxed{ \ Hazel's \ travel = 6x \ }}$

In total, all four travel a total of 888 miles to camp. Meaning, all of the above adds up to 888.

$\boxed{ \ x + 2x + 3x + 6x = 888 \ }$

$\boxed{ \ 12x = 888 \ }$

$\boxed{ \ 12 \cdot x = 888 \ }$

Both sides multiplied by 12.

$\boxed{ \ x = 888 \div 12 \ }$

$\boxed{\boxed{ \ x = 74 \ }}$

We have obtained x. The final step is to substitute the value of x for each person's travel.

• $\boxed{ \ Eli's \ travel = x \rightarrow \boxed{ \ Eli's \ travel = 74 \ miles \ }}$
• $\boxed{ \ Sara's \ travel = 2x \rightarrow \boxed{ \ Sara's \ travel = 2 \times 74 = 148 \ miles \ }}$
• $\boxed{ \ Ashley's \ travel = 3x \rightarrow \boxed{ \ Ashley's \ travel = 3 \times 74 = 222 \ miles \ }}$
• $\boxed{ \ Hazel's \ travel = 6x \rightarrow \boxed{ \ Hazel's \ travel = 6 \times 74 = 444 \ miles \ }}$

Thus we already know how far each of them travels.

- - - - - - -

The summary scheme is as follows:

• Eli's travel ⇒ $\boxed{x}$
• Sara's travel ⇒ $\boxed{x}\boxed{x}$
• Ashley's travel ⇒ $\boxed{x}\boxed{x}\boxed{x}$  
• Hazel's travel ⇒ $\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}$

$\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x} = 888$

$\boxed{ \ 12 \cdot x = 888 \ }$

$\boxed{ \ x = 888 \div 12 \ }$

Hence, the value of x is $\boxed{\boxed{ \ x = 74 \ }}$

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