Posted by (: on Wednesday, October 14, 2009 at 3:39pm.
Lydia wants to buy picnic tables, benches, and permanently installed grills. On one page she notices that 5 picnic tables, 10 benches, and 3 grills sell for $1330. On another page she sees that 20 picnic tables, 30 benches, and 20 grills sell for $5550. Finally, on a third page she sees that 2 picnic tables and 4 benches sell for $430. Help Lydia find the individual prices for the three items. Define three variables, write a system of equations, and solve to find the cost of each item. Justify your answer by showing how you solved the problem, and check the solution.

Algebra  MathMate, Wednesday, October 14, 2009 at 5:23pm
I will give you a kickstart.
Represent each of the items by a symbol, say:
T=picnic tables
B=bench
G=Grill
On the first page: " 5 picnic tables, 10 benches, and 3 grills sell for $1330. "
So 5T+10B+3G = 1330 .....(1)
Continue this way and you should end up with three equations in the three unknowns T, B and G.
Solve the system for Lydia.