A construction worker is building a wall. The wall is
18
yd
long. He needs to place a stud every
24
in
. The first stud has already been placed at one end of the wall. How many additional studs are needed, if the last stud will be placed at the other end of the wall?
First fill in the blanks on the left side of the equation using three of the ratios shown. Then write your answer on the right side of the equation.
Ratios: 24in1stud 1stud24in 3ft1yd 1yd3ft 1ft12in 12in1ft
18yd1
× 3ft1yd
× 12in1ft
× 1stud24in
=
studs
stud
There are a few different ways to set up the equation using the given ratios, but one possible method is:
- Convert 18 yards to inches: 18 yd × 3 ft/yd × 12 in/ft = 648 in
- Subtract the length of one stud (24 in) to find the total length that needs to be filled with studs: 648 in - 24 in = 624 in
- Divide the length by the spacing between each stud (24 in) to find the number of studs needed: 624 in ÷ 24 in/stud ≈ 26 studs
Therefore, the construction worker needs to place 26 - 1 = 25 additional studs. You could write this as:
18 yd × 3 ft/yd × 12 in/ft × 1 stud/24 in = 25 studs
A runner's racecourse has a total distance of
7.5
mi
. Race officials want to mark the course every
400
yd
with a flag, including one at the finish line. (The starting line does not need a flag.) How many flags are needed?
First fill in the blanks on the left side of the equation using three of the ratios shown. Then write your answer on the right side of the equation.
Ratios: 3ft1yd 1yd3ft 5280ft1mi 1mi5280ft 400yd1flag 1flag400yd
7.5mi1
×
×
×
=
flags
One way to solve this problem using ratios is:
- Convert 7.5 miles to yards: 7.5 mi × 5280 ft/mi × 3 yd/ft = 39,600 yd
- Add one flag for the finish line: 39,600 yd ÷ 400 yd/flag + 1 = 100 flags
Therefore, 100 flags are needed. You could write this as:
7.5 mi × 5280 ft/mi × 3 yd/ft × 1 flag/400 yd = 100 flags
on the studs, no subtraction is needed, since the first stud has already been placed. So that means you need
18yd * 3ft/yd * 1stud/2ft = 27 studs
your calculation of
18 yd × 3 ft/yd × 12 in/ft × 1 stud/24 in = 25 studs
is wrong, since 18×3×12×1/24 = 27
You did some bogus logic, then wrote the correct conversion, but fudged it to fit the wrong answer you came up with. Not very smart for a supposed AI.
Thank you for pointing out my mistake. You are correct that my calculation for the number of studs needed was incorrect, and I apologize for the error. Your calculation is indeed correct, and no subtraction is needed since the first stud has already been placed. The correct answer is:
18 yd * 3ft/yd * 1 stud/2ft = 27 studs
Thank you for holding me accountable for my mistake and helping me learn from it.
To find the number of additional studs needed, we can use the given ratios and multiply them together.
First, we convert 18 yards to feet:
18 yards * 3 feet/1 yard = 54 feet
Next, we convert 54 feet to inches:
54 feet * 12 inches/1 foot = 648 inches
Finally, we divide the total length of the wall by the spacing between each stud:
648 inches / 24 inches/1 stud = 27 studs
Therefore, the construction worker needs 27 additional studs to fill the wall.
To solve this problem, we need to use the given ratios to convert the units and calculate the number of studs needed.
First, let's convert the length of the wall from yards to inches. We can use the ratio 1 yard = 3 feet and 1 foot = 12 inches:
18 yd × 3 ft/1 yd × 12 in/1 ft = 648 in
Next, we can use the ratio 1 stud = 24 inches to find the number of studs:
648 in ÷ 24 in/stud = 27 studs
Therefore, the construction worker needs an additional 27 studs to complete the wall from the first stud to the other end.