Joanna went to school supply shopping. She spent $31.80 on notebooks and pencils. Notebooks cost $2.05 each and pencils cost $1.50 each. She bought a total of 19 notebooks and pencils. How many of each did she buy?

A.
11 notebooks; 8 pencils
B.
9 notebooks; 10 pencils
C.
6 notebooks; 13 pencils
D.
4 notebooks; 15 pencils

C

Step-by-step explanation:

Total number of notebooks and pencils= 19

Assuming that she bought notebooks only,

amount spent

= 19($2.05)

= $38.95

Difference in actual amount spent

= $38.95 -$31.80

= $7.15

This difference in amount is due to the number of wrong assumptions we have made previously, such that we assumed that a certain number of pencils that she bought was notebooks. Thus, let's find the number of wrong assumptions so we can find out how many pencils she bought.

Cost difference of each notebook compared to a pencil

= $2.05 -$1.50

= $0.55

This means that for each wrong assumption, there is an additional $0.55 in the total amount Joanna spent.

Number of sets of extra $0.55

= $7.15 ÷$0.55

= 13

Thus, she bought 13 pencils.

Amount of notebooks bought

= 19 -13

= 6

Let's check our work!

If Joanna bought 13 pencils and 6 notebooks,

total amount spent

= 13($1.50) +6($2.05)

= $19.50 +$12.30

= $31.80

Thus option C is indeed correct as it is given from the question that she spent $31.80.

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are