Mrs. Maynard is researching what it would cost to order flower arrangements for a fancy party. She wants one large centerpiece for the head table, and smaller arrangements for the smaller tables. Dayton Florist charges $15 for each smaller arrangement, plus $50 for the large centerpiece. Abby's Flowers, in contrast, charges $40 for the large centerpiece and $20 per arrangement for the rest. If Mrs. Maynard orders a certain number of small arrangements, the cost will be the same at either flower shop. How many small arrangements would that be?

Question

anonymous · Answer

Write a system of equations, graph them, and type the solution.

Would the linear equations be:
15x+50=y and 20x+40=y?

kobeni-chan · Answer

Yes

kobeni-chan · Answer

You can solve for x by setting the two equations equal to each other (since it would cost the same amount). Then you should be able to substitute x back into one of the equations to solve for y.

anonymous · Answer

So 15x+50=20x+40?

kobeni-chan · Answer

Yep :)

anonymous · Answer

X = 2 ?

kobeni-chan · Answer

Yes

anonymous · Answer

Oh okay, so 2 and 80, how would you graph it though?

anonymous · Answer

And thanks!

kobeni-chan · Answer

No problem! 2 and 80 are your coordinates (2, 80). You can substitute values like 1, 3, etc, into one of the equations, solve for y, and then you will get other coordinates that you can graph :)

anonymous · Answer

So if I sub in 1 for 15(1)+50=y I'd get y=65, so then I would graph in (1,65)? and then sub in 1 for the other one 20(1)+40=y and get (1,80)?

kobeni-chan · Answer

Yep :) they will result inintersecting lines on the graph