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musickatia [10]
3 years ago
14

Jon makes a mix of salad that cost $15 using as much apples that cost $4/kg as oranges that cost $6/kg. How much of each fruit i

s in the salad?
Mathematics
2 answers:
alexira [117]3 years ago
7 0
<span>Jon used 1.5 kg of apples and 1.5 kg of oranges. If 1 kg of apples cost $4, then 1.5 kg will cost $6. If 1 kg of oranges costs $6, then 1.5 kg of oranges will cost $9. $6 + $ 9 is equal to $15 which is the total Jon spent.</span>
marysya [2.9K]3 years ago
6 0
Let
 x = number of apples.
 y = number of oranges.
 we have to write the following equation to represent the problem:
 4x + 6y = 15
 To satisfy the equation, Jon must have used
 x = 2.25
 y = 1
 Substituting
 4 (2.25) +6 (1) = 15
 9 + 6 = 15
 answer
 Jhon used 2.25kg of apple and 1kg of orange to make the salad.
 Note: Since the problem does not have any other restrictions, there may be several apple and orange combinations that cost $ 15 per salad.
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Answer:

\displaystyle A_{\text{Total}}\approx45.0861\approx45.1

Step-by-step explanation:

We can use the trigonometric formula for the area of a triangle:

\displaystyle A=\frac{1}{2}ab\sin(C)

Where a and b are the side lengths, and C is the angle <em>between</em> the two side lengths.

As demonstrated by the line, ABCD is the sum of the areas of two triangles: a right triangle ABD and a scalene triangle CDB.

We will determine the area of each triangle individually and then sum their values.

Right Triangle ABD:

We can use the above area formula if we know the angle between two sides.

Looking at our triangle, we know that ∠ADB is 55 DB is 10.

So, if we can find AD, we can apply the formula.

Notice that AD is the adjacent side to ∠ADB. Also, DB is the hypotenuse.

Since this is a right triangle, we can utilize the trig ratios.

In this case, we will use cosine. Remember that cosine is the ratio of the adjacent side to the hypotenuse.

Therefore:

\displaystyle \cos(55)=\frac{AD}{10}

Solve for AD:

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\displaystyle A=\frac{1}{2}ab\sin(C)

Substituting AD for a, 10 for b, and 55 for C, we get:

\displaystyle A=\frac{1}{2}(10\cos(55))(10)\sin(55)

Simplify. Therefore, the area of the right triangle is:

A=50\cos(55)\sin(55)

We will not evaluate this, as we do not want inaccuracies in our final answer.

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We will use the same tactic as above.

We see that if we can determine CD, we can use our area formula.

First, we can determine ∠C. Since the interior angles sum to 180 in a triangle, this means that:

\begin{aligned}m \angle C+44+38&=180 \\m\angle C+82&=180 \\ m\angle C&=98\end{aligned}

Notice that we know the angle opposite to CD.

And, ∠C is opposite to BD, which measures 10.

Therefore, we can use the Law of Sines to determine CD:

\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}

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So, we can substitute 98 for A, 10 for a, 38 for B, and CD for b. Therefore:

\displaystyle \frac{\sin(98)}{10}=\frac{\sin(38)}{CD}

Solve for CD. Cross-multiply:

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Divide both sides by sin(98). Hence:

\displaystyle CD=\frac{10\sin(38)}{\sin(98)}

Therefore, we can now use our area formula:

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We will substitute 10 for a, CD for b, and 44 for C. Hence:

\displaystyle A=\frac{1}{2}(10)(\frac{10\sin(38)}{\sin(98)})\sin(44)

Simplify. So, the area of the scalene triangle is:

\displaystyle A=\frac{50\sin(38)\sin(44)}{\sin(98)}

Therefore, our total area will be given by:

\displaystyle A_{\text{Total}}=50\cos(55)\sin(55)+\frac{50\sin(38)\sin(44)}{\sin(98)}

Approximate. Use a calculator. Thus:

\displaystyle A_{\text{Total}}\approx45.0861\approx45.1

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