Step-by-step explanation:
so, we need to find the smallest common multiple of 36 and 42.
that is the smallest number I can divide both by 36 and 42 without remain.
let's use the method of basic prime factors (we start with the smallest fitting prime number - 2 is a prime number too - and divide as often as possible, then continue with the next bigger prime number, until there is nothing left to divide) :
36 / 2 = 18
18 / 2 = 9
9 / 3 = 3
3 / 3 = 1 finished
therefore,
36 = 2×2×3×3
42 / 2 = 21
21 / 3 = 7
7 / 5 does not work
7 / 7 = 1 finished
therefore,
42 = 2×3×7
to find the smallest common multiple (SCM) we check the maximum length of each prime factor sequence.
and we see 2 times 2, 2 times 3 and 1 time 7.
so, the SCM = 2×2×3×3×7 = 252.
there is no smaller number that can be divided by both 36 and 42 without remain.
so, the rod must be at least 252 cm long to cut it into equally long pieces of either 36 cm (7 pieces) or 42 cm (6 pieces).
Answer:
$ (7x+12)
Step-by-step explanation:
We have that,
Price of each cell phone plan = $x
Since, 3 friends pay extra $4 for the plan.
Thus, the amount paid by the three friends is $ 3(x+4).
Now, as the ramaining people do not pay the extra cost and there are 7-3 = 4 people remaining.
Thus, the amount paid by remaining people = $ 4x
Thus, the total cost of the plan will be $ [3(x+4) + 4x] = $ (7x+12).
Hence, the expression for the total cost of the seven plans is $ (7x+12).
Answer:
3+4p+8t
Step-by-step explanation:
90 ft is less than 32 yards
