Interpret the given information:
At a baseball game, Jose bought five hot dogs and three cans of soda for $17. At the same time, Natasha bought two hot dogs and four cans of sodas for $11.
Let d = cost of a hot dog
Let s = cost of a can of soda
a) 5d + 3s = 17
2d + 4s = 11
4(5d + 3s = 17)
3(2d + 4s = 11)
20d + 12s = 68
6d + 12s = 33
subtract
14d = 35
d = 2.5
s = 1.5
Answer:
b) hot dog:
d = $2.50
c) can of soda: s = $1.50
Check:
5(2.5) + 3(1.5)=17
12.5 + 4.5 = 17
17 = 17 |
2(2.5) + 4(1.5)=11
5 + 6 = 11
11 = 11 |
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d) Interpret the graph:
The blue line is 5d + 3s = 17
s = -5d/3 + 17/3
The red line is 2d + 4s = 11
s = -d/2 + 11/4
hot dogs on x-axis
sodas on y-axis
The point where the lines intersect is the location where the values of d and s make both equations true. It is the point where we find the price of one hotdog, d, and one soda, s. |