While you could use the guess-and-check method, your teacher is more likely to appreciate your work if you write an equation to model this question. Based on the given information, we can write the following equation:
#y=15x+30#
Where #x# represents the number of fruit baskets purchased and #y# represents the total cost in dollars of the membership fee and fruit baskets.
We are given that the total cost of Ms. Williams' purchase is #$105#, and we are asked to find the number of fruit baskets that she purchased. In other words, we are given that #y=105#, and we are asked to find the corresponding value for #x#. So our task here is to substitute #105# into the equation we found above for #y# and solve for #x#:
#color(blue)(y)=15x+30#
#color(blue)(105)=15x+30)#
Now, subtract #30# from both sides of the equation:
#75=15x#
Now, divide both sides of the equation by #15#:
#color(red)(x=5)#
While you might be tempted to put this as your answer, #x=5# is actually not the true answer that your teacher will be looking for, since this is a real world application problem. What your teacher will be looking for is the following statement:
Ms. Williams purchased #5# fruit baskets.
I hope that helps!
