Question:
Lewis directs the school marching band. He uses scale drawings of the football field to design marching formations for the band. The football field is 100 yards long and 53 1/3 yards wide. Lewis always uses a scale of 1 inch to 10 yards for his drawings.
Find the length and width of the football field as it appears in one of Lewis scale drawings.
Answer:
[tex]Length = 10\ inches[/tex]
[tex]Width = 5\frac{1}{3}\ inches[/tex]
Step-by-step explanation:
Given
[tex]Length = 100\ yd[/tex]
[tex]Width = 53\frac{1}{3}\ yd[/tex]
[tex]Scale = 1\ in: 10\ yd[/tex]
Required
Determine the scale measurement
Calculating the length
The ratio of the scale measurement to the actual measurement of the length of the field can be represented as:
[tex]L\ in : 100\ yd[/tex]
Compare this to the scale ratio; we have
[tex]L : 100 = 1\ in: 10\ yd[/tex]
Convert to fraction
[tex]\frac{L}{100\ yd} = \frac{1\ in}{10\ yd}\\[/tex]
Solve for L
[tex]L = 100\ yd * \frac{1\ in}{10\ yd}[/tex]
[tex]L = \frac{100\ in}{10}[/tex]
[tex]L = 10\ in[/tex]
Calculating the length
The ratio of the scale measurement to the actual measurement of the length of the field can be represented as:
[tex]W\ in : 53\frac{1}{3}\ yd[/tex]
Compare this to the scale ratio; we have
[tex]W : 53\frac{1}{3}\ yd = 1\ in: 10\ yd[/tex]
Convert to fraction
[tex]\frac{W}{53\frac{1}{3}\ yd} = \frac{1\ in}{10\ yd}\\[/tex]
Solve for W
[tex]W = 53\frac{1}{3}\ yd * \frac{1\ in}{10\ yd}[/tex]
Convert to improper fraction
[tex]W = \frac{160}{3}\ yd * \frac{1\ in}{10\ yd}[/tex]
[tex]W = \frac{16}{3}\ in[/tex]
[tex]W = 5\frac{1}{3}\ in[/tex]
