Before beginning voice lessons, Elizabeth already knew how to sing 15 pieces, and she expects to learn 2 new pieces during each week of lessons. How many weeks of lessons will Elizabeth need before she will be able to sing a total of 47 pieces?

2 Answers
Oct 31, 2016

16 weeks.

Explanation:

The first step is to find out how many more pieces she needs to learn

47 pieces - 15 pieces ( that she already knows = 32 pieces left to learn

She learns 2 pieces per week, per means to divide so divide 32 by 2

# 32/2 = 16 # It will take 16 weeks for her to learn the 32 new pieces she needs to reach the desired 47 pieces

Oct 31, 2016

So the number of weeks to learn 32 more songs is 16

Explanation:

#color(blue)("Preamble")#

Consider the example of #3/4# this can be written as #6/8# and have the same value. It just looks different.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering your question")#

Total to know# ->47#
Already know#->ul(15) larr" subtract"#
Need to learn#->32#

Using ratio:

#"Given values for ratio"->("learn count")/("week count") -> 2/1#

But we need to learn 32 so we have

#("learn count")/("week count") -> 2/1 -=32/("week count")#

Note that #-=# means 'equivalent to'

#color(brown)("Multiply by 1 and you do not change the overall value. However, 1")##color(brown)("comes in many forms.")#

#("learn count")/("week count") -> [2/1 color(magenta)(xx1 )]-=32/("week count")#

#" "[2/1color(magenta)(xx16/16)]=32/("weeks count")#

#" "[32/16]=32/("weeks count")#

So the number of weeks to learn 32 more songs is 16