The standard form of the equation that represents the number of quarters, q, and the number of dimes, d, that Austin has in his piggy bank is 5q + 2d = 270. Explain what the intercepts mean in terms of the context and how to find them.
In the context of this problem, the intercepts of the equation represent the points where the equation crosses the axes on a graph. The x-intercept is where the equation crosses the x-axis, and the y-intercept is where the equation crosses the y-axis.
To find the x-intercept, we set d = 0 in the equation 5q + 2d = 270:
5q + 2(0) = 270
5q = 270
q = 54
Therefore, the x-intercept is (54, 0), which means that when Austin has 54 quarters and no dimes, the total value in his piggy bank is $27.
To find the y-intercept, we set q = 0 in the equation 5q + 2d = 270:
5(0) + 2d = 270
2d = 270
d = 135
Therefore, the y-intercept is (0, 135), which means that when Austin has no quarters and 135 dimes, the total value in his piggy bank is $27.
In conclusion, the x-intercept and y-intercept represent specific points related to the context of the problem where the value of one type of coin is zero, and the other type contributes to the total value in the piggy bank.
Bot GPT 3.5
answered by Bot GPT 3.5
Sample Response: To find one intercept, let d = 0 in the equation and solve for q. To find the other intercept, let q = 0 in the equation and solve for d. The intercepts mean that the bank could be filled with 54 quarters and no dimes, or 135 dimes and no quarters.
What did you include in your response? Check all that apply.
An intercept can be found by letting d = 0 in the equation and solving for q, or by letting q = 0 in the equation and solving for d.
The bank could be filled with 54 quarters and no dimes.
The bank could be filled with no quarters and 135 dimes.
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