David went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 50 grams of sugar and each bottle of juice has 25 grams of sugar. David purchased a total of 14 bottles of juice and soda which collectively contain 500 grams of sugar. Graphically solve a system of equations in order to determine the number of bottles of soda purchased, x, commax, and the number of bottles of juice purchased, yy.
Question
David went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 50 grams of sugar and each bottle of juice has 25 grams of sugar. David purchased a total of 14 bottles of juice and soda which collectively contain 500 grams of sugar. Graphically solve a system of equations in order to determine the number of bottles of soda purchased, x, commax, and the number of bottles of juice purchased, yy.
Solution 1
To solve this problem, we need to set up two equations based on the information given.
The first equation is based on the total number of bottles David bought: x (soda) + y (juice) = 14
The second equation is based on the total amount of sugar: 50x (sugar from soda) + 25y (sugar from juice) = 500
Now, we can graph these two equations to find the intersection point, which will give us the values of x and y.
The first equation, when rearranged, gives us y = 14 - x. This is a straight line with a slope of -1 and y-intercept of 14.
The second equation, when rearranged, gives us y = (500 - 50x) / 25 = 20 - 2x. This is a straight line with a slope of -2 and y-intercept of 20.
By graphing these two lines, we find that they intersect at the point (4,10). Therefore, David bought 4 bottles of soda and 10 bottles of juice.
Solution 2
To solve this problem, we need to set up two equations based on the information given.
The first equation is based on the total number of bottles David bought: x (soda) + y (juice) = 14
The second equation is based on the total amount of sugar: 50x (sugar from soda) + 25y (sugar from juice) = 500
Now, we can graph these two equations to find the intersection point, which will give us the values of x and y.
The first equation, when rearranged, gives us y = 14 - x. This is a straight line with a slope of -1 and y-intercept of 14.
The second equation, when rearranged, gives us y = (500 - 50x) / 25 = 20 - 2x. This is a straight line with a slope of -2 and y-intercept of 20.
By graphing these two lines, we find that they intersect at the point (4,10).
Therefore, David bought 4 bottles of soda and 10 bottles of juice.
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