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mr Goodwill [35]
3 years ago
14

A teacher has 15 weeks in which to teach six chapters. Write and then solve an equation, showing all work, that represents the n

umber of lessons the teacher must teach per week if there is an average of 8.5 lessons per chapter.
Mathematics
1 answer:
Ahat [919]3 years ago
8 0

Answer:

3.4 lessons per week

Step-by-step explanation:

So to find the number of lessons for 6 chapters we need to multiply 8.5 by 6:

8.5 × 6 = x

x = 51 - so we need 51 lessons to finish six chapters

To find the number of lessons per week, we need to divide the number of lessons by the number of weeks:

y = 51 ÷ 15

y = 3.4

So the teacher needs 3.4 lessons per week to teach 6 chapters in 15 weeks.

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x,\ y,\ z-\text{three numbers}\\\\\left\{\begin{array}{ccc}(x+2z)-y=1&(1)\\z+2x=3&(2)\\x+3y+z=18&(3)\end{array}\right\\\\(2)\\z+2x=3\qquad\text{subtract}\ 2x\ \text{from both sides}\\z=3-2x\qquad(*)\\\\\text{Substitute}\ (*)\ \text{to (1) and (3)}\\\\\left\{\begin{array}{ccc}x+2(3-2x)-y=1&\text{use the distributive property}\\x+3y+(3-2x)=18\end{array}\right

\left\{\begin{array}{ccc}x+(2)(3)+(2)(-2x)-y=1\\x+3y+3-2x=18&\text{subtract 3 from both sides}\end{array}\right\\\left\{\begin{array}{ccc}x+6-4x-y=1&\text{subtract 6 from both sides}\\(x-2x)+3y=15\end{array}\right\\\left\{\begin{array}{ccc}(x-4x)-y=-5\\-x+3y=15\end{array}\right\\\left\{\begin{array}{ccc}-3x-y=-5&\text{multiply both sides by 3}\\-x+3y=15\end{array}\right

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