Eleanor and Max used two rectangular wooden boards to make a set for the school play. 1 board was 6 ft long, the other was 5 1/2 ft long. The 2 boards had equal widths. The total area of the set was 60 3/8 square ft. What was the width?
It's nothing
To find the width of the wooden boards, we need to solve the problem step by step:
1. Given that one board is 6 ft long and the other is 5 1/2 ft long, we need to determine the width (W) of both boards.
2. Let's assume the width of each board is W ft.
3. The area of each rectangular board can be calculated as length multiplied by width. So, the area of the first board is 6 ft * W ft = 6W square ft.
4. Similarly, the area of the second board is (5 1/2 ft) * W ft = 11/2 * W square ft = (11W/2) square ft.
5. The total area of the set is given as 60 3/8 square ft.
6. Therefore, the equation is: 6W + 11W/2 = 60 3/8.
7. To simplify the equation, we can multiply both sides by 2 to eliminate the fraction: 12W + 11W = 120 6/8.
8. Combining the similar terms, the equation becomes: 23W = 120 6/8.
9. Converting the mixed number into an improper fraction, 120 6/8 becomes (968/8) + (6/8) = 974/8.
10. Now, the equation is: 23W = 974/8.
11. To isolate W, we divide both sides of the equation by 23: W = (974/8) / 23.
12. Dividing fractions, we multiply the numerator by the reciprocal of the denominator: W = (974/8) * (1/23).
13. Multiplying the numerators gives 974, and multiplying the denominators gives 8 * 23 = 184.
14. Therefore, W = 974/184.
15. Simplifying the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2: W = (487/92) ft.
16. Hence, the width of the wooden boards is 487/92 ft or approximately 5.29 ft (rounded to two decimal places).
According to the diagram I drew ....
width --- w
5.5(2w) + .5w = 60.375
11.5w = 60.375
w = 5.25 or 5 1/4 ft