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Bezzdna [24]
3 years ago
10

A farmer picked 600 portugals and oranges in total to be sold to the market. There are 3 times as many oranges as there are port

ugals. How many portugals are picked by the farmer?
Mathematics
1 answer:
max2010maxim [7]3 years ago
6 0

Answer:

450 portugals

Step-by-step explanation:

in this question, we are tasked with calculating the number of portugals which are picked by the farmer

Firstly, let the number of portugals picked be p and the number of oranges picked be r.

Thus;

p + r = 600 ••••••••••(i)

Secondly there are 3 times as many oranges as there are portugals;

That would be;

3 * r = p

3r = p. •••••••••(ii)

substitute ii into i

3r + r = 600

4r = 600

r = 600/4

r = 150

P = 3r

p = 3 * 150 = 450

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Step-by-step explanation:  Given in the question that ΔAM is a right-angled triangle, where ∠C = 90°, CP ⊥ AM, AC : CM = 3 : 4 and MP - AP = 1. We are to find AM.

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In the right-angled triangle ACM, we have

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Now,

AM=AP+PM=AP+(AP+1)\\\\\Rightarrow 2AP=AM-1\\\\\Rightarrow 2AP=5x-1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(A)

Now, since CP ⊥ AM, so ΔACP and ΔMCP are both right-angled triangles.

So,

CP^2=AC^2-AP^2=CM^2-MP^2\\\\\Rightarrow (3x)^2-AP^2=(4x)^2-(AP+1)^2\\\\\Rightarrow 9x^2-AP^2=16x^2-AP^2-2AP-1\\\\\Rightarrow 2AP=7x^2-1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(B)

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Thus,

AM=5\times\dfrac{5}{7}=\dfrac{25}{7}=3\dfrac{4}{7}.

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<span>Check the chart for a better understanding:
</span>



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