32×5 = 5× ? . I know 32×5 = 160, but I don't know how to solve the rest
2 answers:
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Answer:
(a) The largest square side is 24 inches
(b) No. of pieces are 14
Step-by-step explanation:
As per the question:
The dimensions of the fabric are
(a)To calculate the side length of the largest square piece, we need to find the Greatest Common Factor (GCF) of the dimensions as:
Therefore,
The GCF of the dimensions =
Therefore, the largest side of a square that can be cut from the fabric is 24 inches.
(b) The no. of pieces of 24 inches that can be cut from the fabric can be given as:
No. of pieces =
No. of pieces = = 14
4, 5, and 7 are mutually coprime, so you can use the Chinese remainder theorem right away.
We construct a number such that taking it mod 4, 5, and 7 leaves the desired remainders:
- Taken mod 4, the last two terms vanish and we have
so we multiply the first term by 3.
- Taken mod 5, the first and last terms vanish and we have
so we multiply the second term by 2.
- Taken mod 7, the first two terms vanish and we have
so we multiply the last term by 7.
Now,
By the CRT, the system of congruences has a general solution
or all integers ,
, the least (and positive) of which is 27.