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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.

5p+10b+3g= 1330-->-4(5p+10b+3g)=-4(1330)
-20p-40b-12g= -5320
20p+30b+20g= 5550
---------------------------
-10b+8g= 230


5p+10b+3g=1330
2p+4b+ 0g?= 430

im not really sure how to set up this problem...please help!

  • Math -

    looks like you have 3 equations:

    5p+10b+3g = 1330 #1
    2p+3b+2g = 555 #2 (I divided all terms by 10)
    p+2b = 215 #3

    from #2 p = 215-2b

    sub into #1 5(215-2b)+10b+3g = 1330
    ---> 1075 - 10b + 10b + 3g = 1330
    g = 85 , that was lucky, the 10b dropped out

    back into #2
    2(215-2b) + 3b + 170 = 555
    solving this, gave me b = 45

    now into #3
    p +90 = 215
    p = 125

    Picnic table costs $125
    Bench costs $45 and
    Grill costs $85

  • Math -

    omg thanks SO much! :)

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