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Write a system of equation, then kinda please solve it.?

A sporting goods store receives a shipment of 124 Golf Bags. The shipment includes two types of bag, full size and collapsible. The full size cost $38.50 each. The collapsible bags cost $22.50 each. The bill for the shipment is $3430. How many of each type of golf bag are in the shipment?

1)... A + B = 124

2)... A(38.50) + B(22.50) = 3430
2)... A + B (22.50)/(38.50) = 3430/(38.50)

1-2)... B - B(22.5)/(38.5) = 124 - 3430/38.5

B (1-22.5/38.5) = 124 - 3430/38.5

B = (124 - 3430/38.5) / (1-22.5/38.5)

B = 84

A = 124 - B = 40

40 full size bags
84 collapsible bags

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