# Kevin wishes to buy apples and bananas, Apples are 50 cents per pound and bananas are 10 cents per pound. Kevin will spend $5.00 for his fruit. How do you write an equation that models this situation and describe the meaning of the two intercepts?

Model

Within the limits :

Let count of apples be:

Let count of bananas be:

Cost of apples per pound (lb) is:

Cost of bananas per pound (lb) is:

Let total cost be:

Then

Given that total cost

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The counts of apples or bananas are not specified so within limits of total cost we can only have so many of each of them. The proportion is controlled by the total cost of $5

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If all apples then the maximum count is for $5 worth:

Thus

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If all bananas then the maximum count is for $5 worth:

Thus

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Using this limiting factor we have:

As we are just dealing with counts drop the $ sign

Subtract 0.1b from both sides

Lets get rid of the decimals: multiply both sides by 10

Divide both sides by 5

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The equation representing the situation is: 0.5x + 0.1y = 5.

The x-intercept represents the number of pounds of apples Kevin can buy if he spends all $5. The y-intercept represents the number of pounds of bananas he can buy if he spends all$5.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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