Answer :
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
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
- 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.
[tex]\boxed{ \ Eli's \ travel = x \ }[/tex]
Sara travels twice as far as Eli.
[tex]\boxed{ \ Sara's \ travel = 2x \ }[/tex]
Ashley travels as far as Sara and Eli together.
[tex]\boxed{ \ Ashley's \ travel = x + 2x \rightarrow \boxed{ \ Ashley's \ travel = 3x \ }}[/tex]
Hazel travels three times as far as Sara.
[tex]\boxed{ \ Hazel's \ travel = 3 \times 2x \rightarrow \boxed{ \ Hazel's \ travel = 6x \ }}[/tex]
In total, all four travel a total of 888 miles to camp. Meaning, all of the above adds up to 888.
[tex]\boxed{ \ x + 2x + 3x + 6x = 888 \ }[/tex]
[tex]\boxed{ \ 12x = 888 \ }[/tex]
[tex]\boxed{ \ 12 \cdot x = 888 \ }[/tex]
Both sides multiplied by 12.
[tex]\boxed{ \ x = 888 \div 12 \ }[/tex]
[tex]\boxed{\boxed{ \ x = 74 \ }}[/tex]
We have obtained x. The final step is to substitute the value of x for each person's travel.
- [tex]\boxed{ \ Eli's \ travel = x \rightarrow \boxed{ \ Eli's \ travel = 74 \ miles \ }}[/tex]
- [tex]\boxed{ \ Sara's \ travel = 2x \rightarrow \boxed{ \ Sara's \ travel = 2 \times 74 = 148 \ miles \ }}[/tex]
- [tex]\boxed{ \ Ashley's \ travel = 3x \rightarrow \boxed{ \ Ashley's \ travel = 3 \times 74 = 222 \ miles \ }}[/tex]
- [tex]\boxed{ \ Hazel's \ travel = 6x \rightarrow \boxed{ \ Hazel's \ travel = 6 \times 74 = 444 \ miles \ }}[/tex]
Thus we already know how far each of them travels.
- - - - - - -
The summary scheme is as follows:
- Eli's travel ⇒ [tex]\boxed{x}[/tex]
- Sara's travel ⇒ [tex]\boxed{x}\boxed{x}[/tex]
- Ashley's travel ⇒ [tex]\boxed{x}\boxed{x}\boxed{x}[/tex]
- Hazel's travel ⇒ [tex]\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}\boxed{x}[/tex]
[tex]\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[/tex]
[tex]\boxed{ \ 12 \cdot x = 888 \ }[/tex]
[tex]\boxed{ \ x = 888 \div 12 \ }[/tex]
Hence, the value of x is [tex]\boxed{\boxed{ \ x = 74 \ }}[/tex]
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Keywords: Sara travels, twice, as far as, Eli, when going to camp, Ashley, Hazel, three times, In total, all four travel, 888 miles, how far, each, substitute
