A formula for this problem can be written as:
#e = (p * h) + (r * b)#
Where:
#e# iw Angel's earnings: $160.25 for this problem.
#p# is Angel's hourly pay rate: $3 per hour for this problem.
#h# is the number of hours Angel worked: What we are solving for in this problem.
#r# is the rate Angel is paid for each ball found: $3.25 for this problem.
#b# is the number of balls found. For this problem we are told Angel found 15 balls per hour so we can write this as: #(15/"hr" * h)#
Substituting and solving for #h# gives:
#$160.25 = (($3)/"hr" * h) + ($3.25 * (15/"hr" * h))#
#$160.25 = (($3)/"hr" * h) + ($3.25 * 15/"hr" * h)#
#$160.25 = (($3)/"hr" * h) + (($48.75)/"hr" * h)#
#$160.25 = (($3)/"hr" + ($48.75)/"hr")h#
#$160.25 = ($51.75)/"hr"h#
#$160.25 xx color(red)("hr")/(color(red)($)color(blue)(51.75)) = ($51.75)/"hr"h xx color(red)("hr")/(color(blue)($)color(blue)(51.75))#
#color(blue)(cancel(color(black)($)))160.25 xx color(red)("hr")/(cancel(color(blue)($))color(blue)(51.75)) = color(blue)(cancel(color(black)($51.75)))/color(red)(cancel(color(black)("hr")))h xx cancel(color(red)("hr"))/cancel((color(blue)($)color(blue)(51.75)))#
#(160.25"hr")/color(blue)(51.75) = h#
#3.1"hr" = h#
Angel worked 3.1 hours rounded to the nearest tenth of an hour.
