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dimulka [17.4K]
3 years ago
15

Mia has $50 on a gift card to her favorite coffee shop. Each time she visits the coffee shops she spends $3.75 on her favorite d

rink. Choose the equation that represents the relationship between x, the number of times she visits the coffee shop, and y, the total amount on her gift card.
Mathematics
1 answer:
kirza4 [7]3 years ago
5 0

Given:

Value of Gift card = $50

Each time she visits the coffee shops she spends $3.75 on her favorite drink.

To find:

The equation for the given situation.

Solution:

Let x be the number of times she visits the coffee shop, and y be the total amount on her gift card.

Cost of her favorite drink for one time = $3.75

Cost of her favorite drink for x times = $3.75x

Value of gift card is $50. So,

Amount on her gift card = 50 - Cost of her favorite drink for x times

y=50-3.75x

Therefore, the required equation is y=50-3.75x.

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Equation is: y = 0.5x² + 0.5x - 3

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y = ax² + bx + c

Now, we will need to solve for a, b and c.
To do this, we will simply get points from the graph, substitute in the general equation and solve for the missing coefficients.

First point that we will use is (0,-3). 
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The equation now becomes:
y = ax² + bx - 3

The second point that we will use is (2,0):
y = ax² + bx - 3
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This means that:
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The third point that we will use is (-3,0):
y = ax² + bx - 3
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0 = 9a - 3b - 3
9a - 3b = 3 ...........> II

Substitute with I in II and solve for a as follows:
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Substitute with the value of a in equation I to get b as follows:
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Substitute with a and b in the equation as follows:
y = 0.5x² + 0.5x - 3

Hope this helps :)
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