Answer :
Problem 1
3 pounds = 12 dollars
3/3 pounds = 12/3 dollars .... divide both sides by 3
1 pound = 4 dollars
4 dollars = 1 pound
4 dollars per pound is the unit price for store A
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Problem 2
The unit price for store B is 2 dollars per pound
The slope of the equation is the same as the unit price. This is because the slope represents the rate of change. Each time x (number of pounds) goes up by 1, the value of y (price) goes up by 2 dollars.
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Problem 3
Start at (0,0). Then move up 3 and to the right 1. We see the slope is 3/1 = 3.
The unit price for store C is 3 dollars per pound
You could also use the slope formula, with points such as (0,0) and (1,3)
m = (y2-y1)/(x2-x1)
m = (3-0)/(1-0)
m = 3/1
m = 3
We get the same slope value.
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We could also look at the y value when x = 1. In this case y = 3 when x = 1. Put another way, the point (1,3) is on the graph. The unit price is always when x = 1 due to "unit" meaning "one".
Saying "3 dollars per pound" is the same as "3 dollars for every one pound".
Side note: this section only works if the line goes through the origin. For any other cases, use the slope method above.
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Problem 4
Store B has the cheapest unit price
There's not much else to say here. All we're doing is comparing the results from problems 1 through 3.
1. At store A the price is $4 per pound. 3 pounds is $12 so 12/3 = $4 for one pound.
2. At store B, the price is $2 for one pound. If you substitute 1 for x and solve the equation, you get 2(1) = $2 per pound.
3. At store C, the graph shows that for 1 pound, the cost is $3.
4. 2<3<4, therefore store B costs the least for one pound of apples.
2. At store B, the price is $2 for one pound. If you substitute 1 for x and solve the equation, you get 2(1) = $2 per pound.
3. At store C, the graph shows that for 1 pound, the cost is $3.
4. 2<3<4, therefore store B costs the least for one pound of apples.