Question

5 students and a teacher stand in aline. If the space between the teacherand the first student is 1.5 meters andthe space between the teacher andthe last students is 6.7 m. If theteacher spaces out the studentsevenly, how much space should therebe between each student? Ignore thespace taken up by the teacher andthe students. Round your answer tothe nearest tenth of a meter.

Answer 1

1.3 meter

Step-by-step explanation

Step 1

Let

red dot = teacher

green dots= students

space between the teacher and the first student is 1.5=black line

space between the teacher and the last students is 6.7 m= blue line

space between each estudent= unknow value= purple line= x

Step 2

make the equation

blue line = blackline + 4*purple line

replace,

`\begin{gathered} 6.7=1.5+(4\cdot x) \\ 6.7=1.5+4x \end{gathered}`

Step 3

solve for x

`\begin{gathered} 6.7=1.5+4\text{x} \\ \text{subtract 1.5 in both sides} \\ 6.7-1.5=1.5+4x\text{ -1.5} \\ 5.2=4x \\ \text{divide each side by }4 \\ (5.2)/(4)=\frac{4x}{} \\ x=1.30 \end{gathered}`

Rounded it is 1.3 meter