Solve the inequality 7y+2<5y+12

Mathematics

1 answer:

Zanzabum2 years ago

3 0

Answer:

y < 5

Step 1: Subtract 5y from both sides.

7y+2−5y<5y+12−5y

2y+2<12

Step 2: Subtract 2 from both sides.

2y+2−2<12−2

2y<10

Step 3: Divide both sides by 2.

$\frac{2y}{2}$ < $\frac{10}{2}$

= y < 5

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Janet can fill a certain order in 5 hours, therefore she performs 1/5 of the order within 1 hour.

Tom needs 8 hours to do the same job, therefore he performs 1/8 of the order within 1 hour.

Working together, they make 1/5 + 1/8 orders within 1 hour.

Let <em>t</em> mean the number of hours they need. Then we have equation:

$\left(\dfrac{1}{5}+\dfrac{1}{8}\right)t=1\\\\_{\text{use}\ \frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}}\\\\\dfrac{(1)(8)+(1)(5)}{(5)(8)}t=1\\\\\dfrac{8+5}{40}t=1\\\\\dfrac{13}{40}t=1\ \ \ \ |\text{multiply both sides by 40}\\\\13t=40\ \ \ \ |\text{divide both sides by 13}\\\\t=\dfrac{40}{13}\\\\t=3\dfrac{1}{13}\\\\Answer:\ 3\dfrac{1}{13}h=3h\ \dfrac{60}{13}min\approx3h\ 5min$