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MATHMAA

# Algebra Student Problems

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1)  Find y when x=1/3 given y=-9x .

Solution:

y=-9(1/3) =-9/3=-3

2) When 30 identical rectangular tables are placed end to end, their perimeter is 306 ft. When the same tables are placed side by side, their perimeter is 190 ft.

a) Write a linear system to model this situation.

b) Solve it.

Solution:

a) Let Length of the table = L

Width of the table =W

Perimeter of rectangle =2L + 2W

30 identical rectangular tables are placed end to end length becomes 30L and width is same W and its perimeter is 306 ft.

2(30L) + 2W = 306
60 L + 2W =306 ------(1)

30 tables are placed side by side , its width changes to 30 W and length remains same L and its perimeter = 190 ft.

2 L + 2(30W) = 190
2L + 60W = 190 -------(2)

Therefore  Linear system model is

60L + 2W =306

2L + 60W =190

b) Solving

60L + 2W =306----------(1)

2L + 60W =190 ---------(2)

Let us use elimination method

multiply (1) by 30 to eliminate W term

1800 L + 60 W =9180

Now subtract (2) from this

1800L + 60W - 2L -60W =9180-190

1798L =8990

L = 8990/1798 =5

Plug L=5 in any one of the equation to get W

60(5) +2W =306

300 + 2W =306

2W=306 -300

2W = 6

W=3

Therefore Length of each table is 5 ft and width is 3 ft.

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