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Quantitative Reasoning – Practice – Form the equation!

PSA_PRACTICE_QNR40. When charging $375 for a catering service they make 25 sales. The owner estimates that if they decrease the price by $10 they will make 2 additional sales.
Is the relationship between sales and price linear? 
What is the slope in the resulting linear equation?
What is the intercept?
What is the equation that relates S, number of sales, and P, price?

Ans:
Let, us assume that they are in linear relationship and can be represented as y=mx+c
where, y= sales & x= price.
According to the question,
25= m(375) + c
27= m(365) + c

Subtracting the above two equations,
2 = -10m
=> m = -(1/5)

Negative slope (-1/5) indicates that as price is reduced the number of sales goes up.

Intercept, c= 25 + (1/5)*375= 25 + 75 = 100

Equation that relates S, number of sales, and P, price:
S= -P/5 + 100
[The above expression takes ‘S’ in the y-axis and ‘P’ in x-axis. We can also express P in terms of ‘S’; however the equation remains same as it is the same line.]

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