+9 Judy wants to make a small patio in her garden. She plans to use pavers. The area of the patio is 2p2 + 30p + 108 square meters, and the area of each paver is p2 + 5p − 6 square meters. The number of pavers Judy will need is given by the expression:
+128475 Total area / area of each paver = the number we need......so
[ 2p^2 + 30p + 108 ] / [ p^2 + 5p - 6] factor top/bottom
[2(p ^2 + 15p + 54)] / [ (p +6)(p-1) ] =
[2 (p + 9) (p + 6)] / [ ( p +6) (p -1) ] =
[2 (p + 9)] / [p - 1] =
[ 2p + 18] / [ p - 1] = the number we need
+118609 Judy wants to make a small patio in her garden. She plans to use pavers. The area of the patio is 2p2 + 30p + 108 square meters, and the area of each paver is p2 + 5p − 6 square meters. The number of pavers Judy will need is given by the expression:
Hi Diva,
Welcome to the forum :)
Do you have any idea how to start this?
I'll hep :)
Say the area of the pavement was 20m^2 and the pavers were 4m^2 then how many pavers would you need?
How did you put 20 and 4 together to get this answer?
If you know how to do it with little numbers then you know what you are supposed to do with the rediculously complicated expressions that you have there.
SO
What do you have to do ? and then.........How might you be able to do it?
+128475 Total area / area of each paver = the number we need......so
[ 2p^2 + 30p + 108 ] / [ p^2 + 5p - 6] factor top/bottom
[2(p ^2 + 15p + 54)] / [ (p +6)(p-1) ] =
[2 (p + 9) (p + 6)] / [ ( p +6) (p -1) ] =
[2 (p + 9)] / [p - 1] =
[ 2p + 18] / [ p - 1] = the number we need
Simplify the following:
(2 p^2+30 p+108)/(p^2+5 p-6)
The factors of -6 that sum to 5 are 6 and -1. So, p^2+5 p-6 = (p+6) (p-1):
(2 p^2+30 p+108)/(p-1) (p+6)
Factor 2 out of 2 p^2+30 p+108:
2 (p^2+15 p+54)/((p+6) (p-1))
The factors of 54 that sum to 15 are 9 and 6. So, p^2+15 p+54 = (p+9) (p+6):
(2 (p+6) (p+9))/((p+6) (p-1))
(2 (p+9) (p+6))/((p+6) (p-1)) = (p+6)/(p+6)×(2 (p+9))/(p-1) = (2 (p+9))/(p-1):
Answer: | (2 (p+9))/(p-1)
