Mrs. Latham ordered 200 SCVCS business cards and paid $23. She ordered 500 business cards a few moths later and paid $35. Write and solve a linear equation to find out how much Mrs. Latham will spend if she orders 700 business cards. Responses$43.00$43.00$42.50$42.50$41.00$41.00$43.75
Question
Mrs. Latham ordered 200 SCVCS business cards and paid 35. Write and solve a linear equation to find out how much Mrs. Latham will spend if she orders 700 business cards. Responses43.0042.5041.00$43.75
Solution
To solve this problem, we first need to understand that the cost of the business cards is a linear function of the number of cards. This means that there is a constant rate at which the cost increases for each additional card.
From the problem, we know two points on this line: (200, 23) and (500, 35). We can use these two points to find the slope of the line, which represents the rate.
The slope m of a line through points (x1, y1) and (x2, y2) is given by the formula m = (y2 - y1) / (x2 - x1).
Substituting the given points, we get m = (35 - 23) / (500 - 200) = 12 / 300 = 0.04. This means that each additional card costs $0.04.
Next, we use the point-slope form of a line to write the equation for the cost C of x business cards: C - 23 = 0.04 * (x - 200).
To find out how much Mrs. Latham will spend if she orders 700 business cards, we substitute x = 700 into this equation and solve for C:
C - 23 = 0.04 * (700 - 200), C - 23 = 0.04 * 500, C - 23 = 20, C = 20 + 23, C = $43.
So, Mrs. Latham will spend 43.00.
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