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Sergeu [11.5K]
2 years ago
10

PLSS HELP ME I NEED IT ASAPP TYSM ILY

Mathematics
1 answer:
Hatshy [7]2 years ago
8 0

Answers:

  • He needs <u>   310   </u> grams of the 99% cocoa brand
  • He needs <u>    590    </u>grams of the 70% cocoa brand

======================================================

Explanation:

Let's label the two brands of chocolate as A and B

  • Brand A is 99% cocoa
  • Brand B is 70% cocoa

Furthermore, define these variables

  • x = amount of brand A
  • y = amount of brand B

The amounts are in grams.

The two amounts must add to 900 grams, so x+y = 900. This can be solved to y = 900-x which we'll use later.

Since we have x grams of brand A, and brand A has 99% cocoa, this means 0.99x represents the amount of pure cocoa from brand A.

Similarly, brand B contributes another 0.70y grams of pure cocoa

Overall, we're dealing with 0.99x+0.70y grams of pure cocoa from the two brands mixed together.

---------------

Rolf needs 900 grams of final product. He wants it to be 80% cocoa, which means 80% of the 900 is going to be pure cocoa

80% of 900 = 0.80*900 = 720

Rolf wants 720 grams of pure cocoa after mixing the two brands together.

So this leads to the second equation: 0.99x+0.70y = 720

---------------

Let's apply substitution to replace y with 900-x

0.99x+0.70y = 720

0.99x+0.70( y ) = 720

0.99x + 0.70( 900-x ) = 720

At this point, we have a single variable in which we can isolate x fully.

0.99x + 0.70( 900-x ) = 720

0.99x + 0.70( 900) + 0.70(-x) = 720

0.99x + 630 - 0.70x = 720

0.29x = 720-630

0.29x = 90

x = 90/(0.29)

x = 310.344827586 which is approximate

Rounding to the nearest full gram, we get x = 310

Use this x value to find y

y = 900-x

y = 900-310.344827586

y = 589.655172414 which is also approximate

y = 590 when rounding to the nearest whole number

---------------

In summary, we have

  • x = 310
  • y = 590

Meaning that Rolf will need <u>310 grams</u> of brand A to mix with <u>590 grams</u> of brand B.

If we plugged those values into x+y = 900, then that equation works out.

If we tried the second equation, then,

0.99x+0.70y = 720

0.99*310+0.70*590 = 720

719.9 = 720

The slight discrepancy is due to the fact we rounded those approximate x and y values to the nearest whole number. We would get better accuracy if we rounded to say the nearest tenth or hundredth.

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Here's what i got:

Answer:

A)

<u><em>2.2 * 10^7</em></u>

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Answer in fraction form: x = 55/4

Answer in decimal form: x = 13.75

Both forms are equivalent, but they say it in a slightly different way.

===========================================================

Work Shown:

AC/QY = CD/YW

(x+5)/15 = 5/4

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Explanations:

  • The first step is possible because the polygons are similar. Similar figures have their corresponding sides be in the same proportion or ratio. Note how side AC has the double red angle (at point A) and a single red angle (point C). The side QY has the same idea in the same order. This is why AC corresponds to QY. The ratio AC/QY is the same as CD/YW.
  • In the second step, I plugged in the expressions that the diagram shows. This is the substitution property.
  • On step 3, I cross multiplied. The general format is A/B = C/D cross multiplies to A*D = B*C.
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