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3 years ago

15

The greater of is 7 more than the lesser. three times the greater number is 5 more than r4 times the lesser number. Find the num

bers

1 answer:

Ilya [14]3 years ago

8 0

<h2>Steps:</h2>

(Let x = greater number and y = lesser number)

So this question is asking us for a system of equations. Using the info they provide, we can form these two equations:

$x=y+7\ \textsf{("The greater of the numbers is 7 more than the lesser.")}\\3x=4y+5\ \textsf{("Three times the greater number is 5 more than 4 times the lesser number.")}$

So for this, we will be using the substitution method. Since we know that x = y + 7, substitute x with (y + 7) in the second equation as such:

$3(y+7)=4y+5$

From here we can solve for y. Firstly, distribute 3 so that it multiplies with y and 7:

$3y+21=4y+5$

Next, subtract 3y on both sides of the equation:

$21=y+5$

Lastly, subtract 5 on both sides of the equation:

$16=y$

Now that we know the value of y, we can substitute it into either equation to solve for x:

$x=16+7\\x=23\\\\3x=4(16)+5\\3x=64+5\\3x=69\\x=23$

<h2>Answer:</h2>

<u>In short, 16 is the lesser number and 23 is the greater number.</u>

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Answer: The correct answer is:

______________

→ Choice: [C]: " $\frac{2}{1} * \frac{7}{-2}$ " .

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Step-by-step explanation:

______________

Note that this problem contains multiplication and division.

WIth multiplication and division;

the order of operations we perform is from "left side to right side" in the expression; in the order in which the operation occurs:

As such:

______________

The given problem:

______________

" $\frac{-3}{4} * \frac{7}{-2}$ ÷ $\frac{3}{-8}$ " ;

Is treated as:

______________

" $(\frac{-3}{4} * \frac{7}{-2})$ ÷ $\frac{3}{-8}$ " ;

______________

So, we start with:

______________

" $\frac{-3}{4} * \frac{7}{-2}$ " ;

______________

→ $\frac{-3}{4} * \frac{7}{-2} = \frac{(-3*7)}{[4*(-2) ]} = \frac{-21}{-8}$ ;

______________

Simplify:

______________

" $\frac{-21}{-8} = \frac{(-1)*21}{(-1) *8}$ " ;

______________

→ The "(-1)'s " cancel out:

{since: "(-1)/(-1) = 1 "} ;

→ And we have: " $\frac{21}{8}$ " ;

______________

Now, continue with the problem, and divide this value by: " $\frac{3}{-8}$ " ;

______________

" $\frac{21}{8}$ ÷ $\frac{3}{-8}$ " ;

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Note that dividing by a number is the same as multiplying by the reciprocal of that said number:

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The reciprocal of " $\frac{3}{-8}$ " ; is: " $\frac{-8}{3}$ : l

As such:

" $\frac{21}{8}$ ÷ $\frac{3}{-8}$ " ;

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= " $\frac{21}{8} * \frac{-8}{3}$ "

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Note: The "8" and the "-8" ;

The "8" can be changed to "1" ; and the "-8" can be changed to "-1" ;

since: "-8 ÷ 8 = 1 " ; and since: "8 ÷ 8 = 1 " ;

Note: The "3" and the "21" ;

The "3" can be changed to "1"; and the "21" can be changed to "7" ;

since: "21 ÷ 3 = 7 " ; and since: "3 ÷ 3 = 1 " ;

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And we can we rewrite the expression:

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→ " $\frac{7}{1} * \frac{-1}{1}$ " ;

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Consider Choice [A]: " $\frac{1}{2} * \frac{7}{2}$ " ; which equals: " $\frac{(1*7)}{(2*2)} = \frac{7}{4} = 1\frac{3}{4}$ " ;

" $1\frac{3}{4} \neq -7$ ."

Rule out: "Choice [A]."

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Consider Choice: [B]: " $\frac{2}{1} * \frac{7}{2}$ " ; which equals: " $\frac{(2*7)}{(1*2)} = \frac{14}{2} = 7$ ; " $7\neq -7$ ."

Rule out: "Choice: [B]."

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Consider Choice: [C]: " $\frac{2}{1} * \frac{7}{-2}$ " ; which equals: " $-7$ ; " $-7 = -7$ ".

Choice [C]: seems correct!

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Consider Choice: [D]: " $\frac{-1}{2} * \frac{7}{-2}$ " ; which equals:

" $\frac{(-1*7)}{(2*-2)} = \frac{-7}{-4} = \frac{(-1)*7}{(-1)*4}$ ;

→ cancel out the "(-1)'s" ;

→ {since: "(-1) / (-1) = 1 " ;

to get:

→ " $\frac{7}{4}$ " ; which equals:

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Rule out: "Choice: [D]."

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The correct answer is:

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Choice: [C]: " $\frac{2}{1} * \frac{7}{-2}$ " .

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Hope this is helpful to you!

Wishing you the best!

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4 0

3 years ago