59.6k views
1 vote
A playing field for the Indoor Football League has a length 26 yards longer than its width. The perimeter of the rectangular field is 164 yards. Find the length and width of the field.

The price of 8 citrons and 9 fragrant wood apples is 121 units. The price of 9 citrons and 8 fragrant wood apples is 117 units. Find the price of a citron and the price of a wood apple.

1 Answer

5 votes

Final answer:

The width and length of the football field are 27 yards and 53 yards, respectively. The price of one citron is 7 units, and one wood apple is 9 units. Additionally, the length of an American football field is 91.4 meters when converted.

Step-by-step explanation:

The student's question involves solving systems of equations and unit conversions which are typically covered in high school mathematics. To solve the field dimensions, we can set up two equations using the given perimeter and the relationship between length and width. For the unit conversions, we use the known conversions between yards, feet, meters, and inches.

  • Let width = W and length = L.
  • From the given information, L = W + 26.
  • The perimeter P is 2L + 2W, so substituting L, we get P = 2(W + 26) + 2W = 164.
  • Solving this equation yields W = 27 yards and thus L = 53 yards.

For the prices of citrons and wood apples, let's designate C as the price of one citron and A as the price of one wood apple. We then have two equations:

  • 8C + 9A = 121
  • 9C + 8A = 117

By solving this system of equations, we find that C = 7 units and A = 9 units.

To convert a football field's length from yards to meters, we use the conversion rate 1 yard = 0.9144 meters. Therefore, a 100-yard field is equivalent to 100 * 0.9144 = 91.44 meters.

A yard consists of 3 feet, so a garden that is 4 yards long is 4 * 3 = 12 feet long. Since one foot equals 12 inches, a width of 4 yards is 4 * 3 * 12 = 144 inches.

User Tyson Hilmer
by
8.9k points