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notsponge [240]
3 years ago
7

The number a is smaller than the number b by 1/5 of b. By what part of a is b bigger than a?

Mathematics
1 answer:
Ira Lisetskai [31]3 years ago
7 0

Answer:

The number b is bigger than the number a by \dfrac{1}{4} of a.

Step-by-step explanation:

1. If the number a is smaller than the number b by 1/5 of b, then

a+\dfrac{1}{5}b=b.

Thus,

a=b-\dfrac{1}{5}b=\dfrac{4}{5}b,\\ \\b=\dfrac{5}{4}a.

2. Consider the expression b=\dfrac{5}{4}a:

b=\dfrac{5}{4}a=\dfrac{4}{4}a+\dfrac{1}{4}a=a+\dfrac{1}{4}a.

This gives you that the number b is bigger than the number a by \dfrac{1}{4} of a.

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Twice a number plus twice a second number is 310. The difference between the numbers is 55
agasfer [191]

Answer:

x = 105

y = 50

Step-by-step explanation:

To solve this, try writing it out as an equation/expression first.

When you do, you should get something like this:

2x + 2y = 310

x - y = 55

This is a system of equations. To solve this, we're going to multiply the second equation [x - y = 55] by 2.

2(x - y = 55) = 2x - 2y = 110

Now, subtract your new equation from the first one [2x + 2y = 310]

2x + 2y = 310

-2x + 2y = -110

//<em>If you</em>'<em>re wondering why I changed the signs of the new equation, I multiplied our new equation [2x - 2y = 110] by -1 since we're subtracting//</em>

When you're done subtracting, the "2x" and "-2x" cancel out, so you're left with:

4y = 200

Now, simply solve for "y" by dividing both sides by 4.

4y = 200

y = 50

Now that we know y's value, substitute it into one of our original equations to solve for x.

//<em>I'm gonna plug y into the second equation [x - y = 55] just because it's easier, but you can plug it into the first one as well and get the same answer//</em>

When we plug it in, we get:

x - (50) = 55

To solve for "x," we must get rid of "-50." To do this, add 50 to both sides.

x - 50 = 55

x = 105

<u>So, x = 105 and y = 50</u>

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:


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Step-by-step explanation:

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