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SCORPION-xisa [38]

3 years ago

9

Bella started her own business. One weekend she sold 3 regular and 9 fluffy slimes for $84. The next weekend she sold 4 regular

and 2 fluffy slimes for $53.50. How much does she sell each type of slime for?

1 answer:

BARSIC [14]3 years ago

3 0

Answer:

$5.85 = cost for fluffy slime

4r + 2(5.85) = 53.5

Step-by-step explanation:

Let r = cost of regular

f = cost of fluffy

(1) 3r + 9f = 84 (2) 4r + 2f = 53.5

4 x (1) 12r + 36f = 336

-3 x (2) <u> -12r - 6f = -160.5</u>

30f = 175.5

f = $5.85 = cost for fluffy slime

4r + 2(5.85) = 53.5

4r + 11.7 = 53.5

4r = 41.8

r = $10.45 = cost for regular

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The relationship between the percentage of frozen citrus crop, and the cost of box of oranges is an illustration of a linear function.

<em>The linear equation of the function is: </em> $g(P) =22.9P +7$ <em>, while its inverse is: </em> $g^{-1}(c) = \frac{c - 7}{22.9}$ <em>.</em>
<em>The domain is from 0% to 100%, while the range is from 7 to 29.9</em>

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Given that:

$c = g(P)$

<u>Input and Output quantity</u>

The input quantity is the <em>percentage of frozen citrus crop</em>, while the output quantity is the <em>cost of box of oranges</em>

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The given parameters can be written as:

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So, we have:

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$m = \frac{13.74}{60\%}$

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The equation is then calculated using:

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$g(P) =22.9P +7$

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The domain is the <em>possible input value (i.e. possible values of P).</em>

Because P is a percentage, its possible values are 0% to 100%.

Hence, the domain of the function is: $[0\%,100\%]$

The range is the <em>possible output value (i.e. possible values of c).</em>

When P = 0% and 100%

$c = 22.9 \times 0\% + 7 = 7$

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$g^{-1}(12)$ is an inverse equation, where 12 represents the <em>cost of box of oranges.</em>

So, $g^{-1}(12)$ represents the percentage of frozen citrus crop, when the cost is $12.

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