goodyear2013 wrote:

Danny spends $360 buying his favorite dolls. If he buys only small LemonHead dolls, which are $1 cheaper than the large LemonHead dolls, he could buy 5 more dolls than if he were to buy only large LemonHead dolls. How much does a large LemonHead doll cost?

A. $5

B. $6

C. $7.2

D. $8

E. $9

Let p $ be the price of large lemonhead doll and n be the no. dolls danny can buy

so we have n*p=360

also if price of 1 dollar less then danny can buy 5 more small head dolls so

(p-1)*(n+5)=360=pn..

pn +5p-n-5=pn or 5p= 5+n or \(5p=5+\frac{360}{p}\)

5p^2-360-5p=0

or p^2-p-72=0

p^2-9p+8p-72=0

or p =9 or -8 (price cannot be negative so p =9

note that the problem can be solved by plugging as well..

Starting with D...because C is not great option to start with here

if p=8 then danny can buy 45 large head dolls and p-1=7 $, he can buy \(\frac{360}{7}\neq{Integer}\)So drop this option

Look at p=9 so Large head dolls=40 and for p-1=$8, then he can buy 45 dolls which is exactly what q. stem says..

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