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2 years ago

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Mr. Rozario bought some oranges and some apples. The ratio of oranges to apples is 2:5. He gave 3/4 to his sister and 34 oranges

to his brother. He now has a ratio of 2:3. How many oranges and apples did he buy?

1 answer:

madam [21]2 years ago

6 0

Answer:

He bought 544 oranges and 1,360 apples

Step-by-step explanation:

Here, we want to know the number of oranges and apples bought

Let the number of oranges be x and the number of apples be y

Looking at their ratios;

x:y = 2:5

so;

x/y = 2/5

2y = 5x ••••••(i)

Now, he lost 3/4 of the apples ( by giving out)

What would be left with him is (1-3/4) = 1/4 * y = 0.25y

What is left with him out if the oranges will be; x-34

So now;

0.25y/x-34 = 2/3

3(0.25y) = 2(x-34) •••••••(ii)

From i, y = 5x/2 = 2.5x

Putting this into ii above, we have

3(0.25)(2.5x) = 2x - 68

1.875x = 2x-68

2x-1.875x = 68

0.125x = 68

x = 68/0.125

x = 544

But y = 2.5x

y = 2.5 * 544 = 1,360

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3 years ago

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<h2>The missing measures of the angles are:</h2>

$m\angle 1= 60^{\circ}\\\\m\angle 2= 39^{\circ}\\\\m\angle 3= 21^{\circ}\\\\m\angle 4 = 39^{\circ}\\\\m\angle 5 = 21^{\circ}$

<u>Given</u>:

$m\angle Z = 138^{\circ}$

<em><u>Note the following:</u></em>

An equilateral triangle has all its three angles equal to each other. Each angle = $60^{\circ}$ .

This implies that, since $\triangle WXY$ is equilateral, therefore, $m\angle Y = m\angle XWY = m\angle XYW = 60^{\circ}$

Base angles of an isosceles triangle are congruent to each other.

This implies that, since $\triangle WZY$ is isosceles, therefore, $m\angle 3 = \angle 5$

Applying the above stated, let's find the measure of each angle:

Find $m\angle 1$

$m\angle 1 = 60^{\circ}$ (an angle in an equilateral triangle equals 60 degrees)

Find $m\angle 2$

$m\angle 2 = 60 - m \angle 3$

$m\angle 2 = 60 -\frac{1}{2}(180 - 138)$ $(Note: \frac{1}{2}(180 - 138) = 1 $ base $ angle $ of $ \triangle WZY)$

$m\angle 2 = 60 -21\\\\m\angle 2 = 39^{\circ}$

Find $m\angle 3$ and $m\angle 5$ (base angles of isosceles triangle WZY)

$m\angle 3 = \frac{1}{2}(180 - 138) (1 $ base $ angle $ of $ \triangle WZY)$

$m\angle 3 = \frac{1}{2}(42) \\\\m\angle3 = 21^{\circ}$

$m\angle3 = m\angle 5$ (base angles of isosceles triangle are congruent)

Therefore,

$m\angle5 = 21^{\circ}$

Find $m\angle 4$

$m\angle 4 = 60 - m\angle 5$

Substitute

$m\angle 4 = 60 - 21\\\\m\angle 4 = 39^{\circ}$

The missing measures of the angles are:

$m\angle 1= 60^{\circ}\\\\ m\angle 2= 39^{\circ}\\\\m\angle 3= 21^{\circ}\\\\m\angle 4 = 39^{\circ}\\\\m\angle 5 = 21^{\circ}$

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