# Algebra

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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 -

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.

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