Automatic Umbrella
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PLEASE HELP ME IN SOLVING THE LINEAR EQUATION?
2) The matrix below gives the number of automatic and manual opening umbrellas sold at a shop in 1985 and 1995. use linear model to represent the sales of each type of umbrella. let t=0 correspond to 1985. Estimate when the number of automatic umbrellas sold equaled the number of manual umbrellas sold
the matrix looks like this:
1985|1995
automatic: 10|20
manual: 25|10
Let a(t) and m(t) denote the sales for the automatic and manual umbrellas, respectively. We are given that a(t) and m(t) are linear functions.
Notice that (0, 10) and (10, 20) must be on the graph of a(t). Similarly, both (0, 25) and (10, 10) must be on the graph of m(t).
By the point-slope formula
a(t) = t + 10
m(t) = -1.5t + 25
If a(t) = m(t), then t = 6. Therefore, the number of automatic umbrellas sold equaled the number of manual umbrellas sold in 1991.
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