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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 4 travel a total of 888 miles to camp. How far do each of them travel?

Sagot :

IwAsSoMeGuY
Eli travels the shortest distance, so she'll be the main letter for algebra. She can be 'e'.
Sara travels twice as far, so her distance is 2e.
Ashley travels Sara and Eli, so 2e + e, or 3e
Hazel travels 3 times Sara, so 2e * 3, or 6e. Together they all travel 888 miles.
So e + 2e + 3e + 6e = 888
Simply, 12e = 888
Therefore, e = 888/12, or 74
So Eli travels 1*74 (74) miles
Sara travels 2*74 (148) miles
Ashley travels 3*74 (222) miles
Hazel travels 6*74 (444) miles
johanrusli

Eli travels 74 miles

Sara travels 148 miles

Ashley travels 222 miles

Hazel travels 444 miles

Further explanation

Simultaneous Linear Equations could be solved by using several methods such as :

  • Elimination Method
  • Substitution Method
  • Graph Method

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

Let :

Sara's Distance = s

Eli's Distance = e

Ashely's Distance = a

Hazel's Distance = h

Sara travels twice as far as Eli when going to camp.

[tex]s = 2e[/tex]

Ashley travels as far as Sara and Eli together.

[tex]a = s + e = 2e + e = 3e[/tex]

Hazel travels 3 times as far as Sara.

[tex]h = 3s = 3(2e) = 6e[/tex]

In total, all 4 travel a total of 888 miles to camp.

[tex]s + a + h + e = 888[/tex]

[tex]2e + 3e + 6e + e = 888[/tex]

[tex](2 + 3 + 6 + 1)e = 888[/tex]

[tex]12e = 888[/tex]

[tex]e = 888 \div 12[/tex]

[tex]e = \boxed {74 ~ \texttt{miles}}[/tex]

[tex]s = 2e = 2(74) = \boxed {148 ~ \texttt{miles}}[/tex]

[tex]a = 3e = 3(74) = \boxed {222 ~ \texttt{miles}}[/tex]

[tex]h = 6e = 6(74) = \boxed {444 ~ \texttt{miles}}[/tex]

Learn more

  • Perimeter of Rectangle : https://brainly.com/question/12826246
  • Elimination Method : https://brainly.com/question/11233927
  • Sum of The Ages : https://brainly.com/question/11240586

Answer details

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations

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