Answer: C
Step-by-step explanation:
Let the unknown number be y.
We can list the equation out by the clues given.
5y + 12 = 52
Then solve this as simple algebra!
Shift +12 to the other side and be - 12
5y = 52-12
5y = 40
Shift x5 to the other side and be ÷5
y = 40 / 5
y = 8
Therfore the unknown number is 8.
The question is essentially asking for the least common multiple of 20 and 25. There are several ways you can find the LCM. One easy way is to divide the product by the GCD (greatest common divisor).
GCD(20, 25) = 5 . . . . . see below for a way to find this, if you don't already know
LCM(20, 25) = 20×25/GCD(20, 25)
... = 500/5 = 100
The buses will be there together again after ...
... B. 100 minutes
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You can also look at the factors of the numbers:
... 20 = 2²×5
... 25 = 5²
The least common multiple must have factors that include all of these*, so must be ...
... 2²×5² = 100
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* you can describe the LCM as the product of the unique factors to their highest powers. 20 has 2 raised to the 2nd power. 25 has 5 raised to the 2nd power, which is a higher power of 5 than is present in the factorization of 20. Hence the LCM must have 2² and 5² as factors.
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You can also look at the factorization of 20 and 25 to see that 5 is the only factor they have in common. That is the GCD, sometimes called the GCF (greatest common factor).
