SOLUTION: An electronics store sells an item costing $51 for $70 and an item costing $120 for $129. If the markup policy of the store is assumed to be linear, write an equation that expresse

Question 1194479: An electronics store sells an item costing $51 for $70 and an item costing $120 for $129. If the markup policy of the store is assumed to be linear, write an equation that expresses the retail price R in terms of the cost C (wholesale price), then solve for R.
(a) R=
Your answer above should represent the retail price in terms of the variable C.
(b) What does a store pay for an item that retails for $135? Give an exact answer.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
straight line equation is y = mx + b.
m is the slope.
b is the y-intercept.
points on the line are in (x,y) format.
(x1,y1) = (51,70)
(x2,y2) = 120,129)
slope = (y2-y1) / (x2-x1) = (129-70) / (120-51) = 59 / 69.
equation becomes y = 59/69 * x + b
solve for b by replacing x and y with the value from one of the points.
equation becomes:
70 = 59/69 * 51 + b
solve for b to get:
b = 70 - (59/69 * 51) = 1821/69
equation becomes:
y = 59/69 * x + 1821/69
when x = 51, y = 70
when x = 120, y = 129
this confirms the equation is correct.
when y = 135, use the equation to solve for x.
y = 59/69 * x + 1821/69 becomes:
135 = 59/69 * x + 1821/69.
solve for x to get:
x = (135 - 1821/69) / (59/69) = (135*69 - 1821) / 59 = 7494 / 59.
in decimal format, that is equal to 127.0169492.
the exact answers are in fraction format.
i graphed the equation of y = 51/69 * x + 1821/69.
it shows that when x = 51, y = 70, and when x = 120, y = 129, and when x = 7494/59, y = 135.
note that, on the graph, x = 7494/59 is shown as 127.017.

answers to your questions are below:

An electronics store sells an item costing $51 for $70 and an item costing $120 for $129. If the markup policy of the store is assumed to be linear, write an equation that expresses the retail price R in terms of the cost C (wholesale price), then solve for R.
Your answer should represent the retail price in terms of the variable C.

(a) R = 59/69 * C + 1821/69
this is derived from the equation y = 59/69 * x + 1821/69 where:
R takes the place of y.
C takes the place of x.

(b) What does a store pay for an item that retails for $135? Give an exact answer.
the store pays 7494 / 59 for an item that sells for 135.

let me know if you have any questions.
theo

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