First, we want to turn the words into math equations. For equation #(1)#, let's set it equal to Roberto's piggy bank #(y)#
#y=5x+30#
He starts off with #$30# and adds #5# every week, or #5x# where #x# is in weeks.
The second equation for Jack this time, is he has #0# starting cash, and adds #$8# every week or #8x#, so his equation is
#y=8x+0#
Next, set these two equations equal to each other to find out how many weeks #(x)# the boys will have to wait to have the exact same amount of money.
#5x+30=8x#
Subtract #5x# from both sides to keep it equal.
#30=3x#
Divide by #3# on both sides
#10=x#
And you have your answer! After #10# weeks, they will both have the same amount of money.
