Question

Maria thinks of a number and subtracts 5\2 from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?​

Answer 1

Answer:

Given :-

• Maria thinks of a number and subtracts 5/2 from it.
• She multiplies the result by 8.
• The result now obtained is 3 times the same number she thought of.

To Find :-

• What is the number.

Solution :-

Let,

$\mapsto \bf The\: number\: Maria\: thought =\: x$

Now,

$\bigstar$ She subtracts 5/2 from that number.

$\implies \sf Number - \dfrac{5}{2}$

$\implies \sf\bold{\purple{x - \dfrac{5}{2}}}$

Again,

$\bigstar$ She multiples the result by 8.

$\implies \sf 8 \times \bigg(x - \dfrac{5}{2}\bigg)$

$\implies \sf\bold{\purple{8\bigg(x - \dfrac{5}{2}\bigg)}}$

According to the question,

$\bigstar$ The result now obtained is 3 times the same number she thought of.

$\implies \sf 8\bigg(x - \dfrac{5}{2}\bigg) =\: 3 \times x$

$\implies \sf 8x - \dfrac{40}{2} =\: 3x$

$\implies \sf \dfrac{16x - 40}{2} =\: 3x$

By doing cross multiplication we get,

$\implies \sf 16x - 40 =\: 2(3x)$

$\implies \sf 16x - 40 =\: 6x$

$\implies \sf 16x - 6x =\: 40$

$\implies \sf 10x =\: 40$

$\implies \sf x =\: \dfrac{4\cancel{0}}{1\cancel{0}}$

$\implies \sf x =\: \dfrac{4}{1}$

$\implies \sf\bold{\red{x =\: 4}}$

${\small{\bold{\underline{\therefore\: The\: number\: that\: Maria\: thought\: is\: 4\: .}}}}$

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★ VERIFICATION ★

$\leadsto \sf 8\bigg(x - \dfrac{5}{2}\bigg) =\: 3x$

By putting x = 4 we get,

$\leadsto \sf 8\bigg(4 - \dfrac{5}{2}\bigg) =\: 3(4)$

$\leadsto \sf 32 - \dfrac{40}{2} =\: 3 \times 4$

$\leadsto \sf \dfrac{64 - 40}{2} =\: 12$

$\leadsto \sf \dfrac{\cancel{24}}{\cancel{2}} =\: 12$

$\leadsto \sf \dfrac{12}{1} =\: 12$

$\longrightarrow \bf 12 =\: 12$

Hence, Verified.

Answer 2

Answer:

Given :-

• Maria thinks of a number and subtract 5/2 from it .She multiplies the result by 8 .The result now obtained is 3 times the same number she thought of.

○To prove :-

• What is the number.

○Explanation :-

• Here let the number Maria thought be x
• According to the given question,
• She subtracts 5/2 from the number it becomes,
• $= x - \frac{5}{2}$

○And ,

• She multiplies number by 8 it becomes,

• $= 8 \times ( x - \frac{5}{2} )$
• $= 8(x - \frac{5}{2} )$

○From the question,

• The result is obtained by 3 times it becomes,
• $8(x - \frac{5}{2} ) = 3 \times x$
• 8x-40/2=3x
• 16x-40x/2=3x

• By equating this equation we get that,
• 16x-40=2 (3x)
• 16x-6x=40
• 10x =40
• $x = \frac{40}{10} = x = 4$

○Therefore,

• The number that maria thought is 4.

○Hope it helps u mate .

○Thank you .