The cost of pen and colored pencils per piece is =10.85
The new total length of both Betty and Beth is =227.2cm
Total number of pens Randy needs to buy = 5
Total number of colored pencils Randy needs to buy= 3
The both items are bought at the same prize = a
The cost of five pens is = 5× a = 5a
The cost of colored pencils is = 3 × a= 5a
The money needed to spend on the items= 86.78
To find the cost of each item which is a ,
5a + 3a = 86.78
(5+3) a= 86.78
8a = 86.78
therefore a = 86.78/8
= 10.85
Therefore the prize of each item is = 10.85. That is option B
Betty's height = 119.2 cm
Beth's height = 105.6cm ( which remained the same)
But Betty's height after 6 months = (6× 0.4) + 119.2
= 2.4 + 119.2
= 121.6 cm
Therefore, the total new height= 121.6 + 105.6
= 227.2cm
That is option A.