Two numbers sum to 56. thrice the first subtracted from the second is 4. find the numbers?

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Two numbers sum to 56. thrice the first subtracted from the second is 4. find the numbers?

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Answer 1 · 2018-06-27T22:25:39

The two numbers are $13$ $13$ and $43$ $43$ .

Explanation:

There are two numbers. Let's call them $x$ $x$ and $y$ $y$ .

$x + y = 56$ $x + y = 56$

Thrice the first subtracted, so $- 3 x$ $-3x$ , from the second, $y$ $y$ , is $= 4$ $= 4$ , so

$y - 3 x = 4$ $y - 3x = 4$

Now you have a simultaneous equation to work with.

$y + x = 56$ $y + x = 56$

$y - 3 x = 4$ $y - 3x = 4$

Same signs subtract, Different signs add. I always prefer dealing with the number after the operation, so I'll start with that. We should make the coefficients the same.

$3 (y + x) = 3 (56)$ $3(y+x) = 3(56)$
$y - 3 x = 4$ $y - 3x = 4$

$3 y + 3 x = 168$ $3y + 3x = 168$
$y - 3 x = 4$ $y - 3x = 4$

If we add the bottom to the top, we end up with

$4 y = 172$ $4y = 172$

$y = \frac{172}{4}$ $y = 172/4$

$y = 43$ $y = 43$

Substitute your answer for $y$ $y$ into any of the equations given (and never the one that you made, in case it is wrong).

Let's take the given one.

$x + y = 56$ $x + y = 56$

$x + 43 = 56$ $x + 43 = 56$

$x = 56 - 43$ $x = 56-43$

$x = 13$ $x = 13$

Therefore,

${(x = 13), (y = 43) :}$

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Two numbers sum to 56. thrice the first subtracted from the second is 4. find the numbers?

1 Answer

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