One number is five bigger than another number.When three times the larger number is added to twice the smaller number the result

is 60 what are the two numbers?(HELP NEEDED FAST)the numbers are
A)9 and 14
B)10 and 15
C)11 and 16
D)12 and 17

Mathematics

1 answer:

Alex73 [517]3 years ago

7 0

$9 \cdot 2+14 \cdot 3= 18+42=60 \\ answer \ A)$

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Multiply.

Crank

The main rules that we use here are :

i) $\sqrt{a \cdot b}= \sqrt{a} \cdot \sqrt{b}$ for nonnegative values a and b.

ii) $\sqrt{a} \cdot \sqrt{a} =a$ .

Thus, first 'decompose' the numbers in the radicals into prime factors:

$4 \sqrt{3} \cdot 10 \cdot \sqrt{2\cdot2\cdot3}\cdot \sqrt{2\cdot 3}\cdot \sqrt{2}.$ .

By rule (i) we write:

$4 \sqrt{3} \cdot 10 \cdot \sqrt{2}\cdot \sqrt{2}\cdot \sqrt{\cdot3}\cdot \sqrt{2} \cdot \sqrt{3} \cdot \sqrt{2}$ .

We can collect these terms as follows:

$40 \sqrt{3}\cdot (\sqrt{3}\cdot \sqrt{3}) \cdot (\sqrt{2}\cdot \sqrt{2}) \cdot( \sqrt{2} \cdot \sqrt{2})$ , and by rule (ii) we have:

$40 \sqrt{3}\cdot 3 \cdot 2 \cdot2=40\cdot12\cdot \sqrt{3}=480 \sqrt{3}.$

Answer: $480 \sqrt{3}$ .