Carl needed exactly 75 m of cloth to make 16 small identical flags and 8 big identical flags. He had some cloth which was just enough to make all the small flags and 4 big flags. He used 120 1/2 cm for each small flag.
(a) How much cloth would he need to make 1 big flag?
(b) How much cloth was he short of to make the remaining big flags?
To make 16 small flags, Carl used a total of 16 x 120 1/2 cm = 1928 cm of cloth.
To make 8 big flags, he used a total of 75 m x 100 cm/m = 7500 cm - 1928 cm = 5572 cm.
To make one big flag, he would need 5572 cm / 8 = 697.75 cm of cloth (rounded to two decimal places).
He was short of cloth to make 8 - 4 = 4 big flags.
To make 4 big flags, he needed a total of 4 x 697.75 cm = 2791 cm of cloth.
Therefore, he was short of 2791 cm - (7500 cm - 1928 cm) = 731 cm of cloth to make the remaining big flags.
To find the amount of cloth needed to make 1 big flag, we need to first find the total amount of cloth used for all the small flags.
The total amount of cloth used for all the small flags can be calculated by multiplying the number of small flags (16) by the amount of cloth used for each small flag (120 1/2 cm).
Total amount of cloth used for small flags = 16 * 120 1/2 cm
To simplify the calculation, convert 120 1/2 cm to a mixed fraction:
120 1/2 cm = 120 cm + 1/2 cm = 120 2/2 cm
Now substitute the mixed fraction into the equation:
Total amount of cloth used for small flags = 16 * 120 2/2 cm
Next, simplify the mixed fraction:
120 2/2 cm = 120 cm + 1 cm = 121 cm
Substituting the simplified fraction, we have:
Total amount of cloth used for small flags = 16 * 121 cm
Now calculate the total amount of cloth used for small flags:
Total amount of cloth used for small flags = 16 * 121 cm = 1936 cm
To find the amount of cloth needed to make 1 big flag, subtract the amount of cloth used for small flags from the total amount of cloth needed:
Amount of cloth needed for 1 big flag = Total amount of cloth needed - Total amount of cloth used for small flags
Amount of cloth needed for 1 big flag = 75 m * 100 cm/m - 1936 cm
Since 1 meter equals 100 centimeters, we can convert 75 meters to centimeters:
75 m * 100 cm/m = 7500 cm
Substituting the values:
Amount of cloth needed for 1 big flag = 7500 cm - 1936 cm
Amount of cloth needed for 1 big flag = 5564 cm
Therefore, Carl would need 5564 cm of cloth to make 1 big flag.
To find the amount of cloth Carl was short of to make the remaining big flags, subtract the amount of cloth used for the 4 big flags from the total amount of cloth needed:
Amount of cloth short to make the remaining big flags = Total amount of cloth needed - Total amount of cloth used for 4 big flags
Amount of cloth short to make the remaining big flags = 75 m * 100 cm/m - 4 * 5564 cm
Again, convert 75 meters to centimeters:
75 m * 100 cm/m = 7500 cm
Substituting the values:
Amount of cloth short to make the remaining big flags = 7500 cm - 4 * 5564 cm
Amount of cloth short to make the remaining big flags = 7500 cm - 22256 cm
Amount of cloth short to make the remaining big flags = -14756 cm
Therefore, Carl was short of 14756 cm of cloth to make the remaining big flags.
To find the answers to these questions, we can follow these steps:
Step 1: Calculate the total cloth used for making all the small flags.
Since Carl used 120 1/2 cm for each small flag, we can find the total cloth used for all the small flags by multiplying the cloth used for one small flag by the total number of small flags.
Total cloth used for all the small flags = (cloth used for one small flag) × (total number of small flags)
Step 2: Calculate the cloth used for the made big flags.
We are given that Carl used some cloth which was just enough to make all the small flags and 4 big flags. Therefore, the cloth used for the made big flags is the cloth used for making all the flags (from step 1) minus the total cloth used for all the small flags.
Cloth used for the made big flags = Total cloth used for all the flags - Total cloth used for all the small flags
Step 3: Calculate the cloth used for one big flag.
To find the cloth used for one big flag, we can divide the cloth used for the made big flags (from step 2) by the number of made big flags.
Cloth used for one big flag = Cloth used for the made big flags / Number of made big flags
Step 4: Calculate the remaining cloth needed for the remaining big flags.
To find this, we can calculate the cloth needed for one big flag (from step 3) and multiply it by the number of remaining big flags.
Remaining cloth needed for the remaining big flags = Cloth used for one big flag × Number of remaining big flags
Now we can find the answers to the given questions:
(a) How much cloth would he need to make 1 big flag?
We can use the result from step 3 to answer this question.
(b) How much cloth was he short of to make the remaining big flags?
We can use the result from step 4 to answer this question.