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IrinaK [193]
3 years ago
10

A florist orders sunflowers every 6 days, starting from the sixth day of the year, and daisies every 4 days, starting from the f

ourth day of the year. When (or on which day) will she orders both kinds of flowers on the same day? *
Mathematics
1 answer:
kolezko [41]3 years ago
8 0

Answer: 12th day

Step-by-step explanation:

Given , A florist orders sunflowers every 6 days and  daisies every 4 days.

When it started from same day, then the next day she orders both kinds of flowers on the same day will be LCM (6,4), where LCM = Least Common Multiple.

Prime factorization:

6 = 2 x 3

4 = 2 x 2

LCM(6,4) = 2 x 2 x 3 = 12

Hence, she will order both kinds of flowers every 12 days.

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Answer:

\huge\boxed{14\ \text{and}\ 7}

Step-by-step explanation:

n,\ m-\text{positive integer}\\\\n=2m-\text{a positive integer is twice another}\\\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}-\text{the sum of the reciprocal of the two positive integer is }\ \dfrac{3}{14}\\\\\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}n=2m&(1)\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}&(2)\end{array}\right

\text{Substitute (1) to (2):}\\\\\dfrac{1}{2m}+\dfrac{1}{m}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{1\cdot2}{m\cdot2}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{2}{2m}=\dfrac{3}{14}\\\\\dfrac{1+2}{2m}=\dfrac{3}{14}\\\\\dfrac{3}{2m}=\dfrac{3}{14}\Rightarrow2m=14\qquad\text{divide both sides by 2}\\\\\dfrac{2m}{2}=\dfrac{14}{2}\\\\\boxed{m=7}

\text{Substitute it to (1):}\\\\n=2\cdot7\\\\\boxed{n=14}

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