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3 years ago

You buy 4 balloons and 2 banners for $8. Your friend buys 6 balloons and 1 banner for $8.

Mathematics

1 answer:

vladimir1956 [14]3 years ago

7 0

Answer:

Each balloon costs $1

Each banner costs $2

Step-by-step explanation:

First of all, let's write down the equation from this problem.

Let "y" be the cost of the ballon, and let "x" be the cost of a banner. Then the following is true from the question...

4y + 2x = 8

6y + x = 8

Now since both of them are equal to 8 both of them are equal to each other, and so we can get the following equation...

4y + 2x = 6y + x

2x - x = 6y - 4y

x = 2y

Now if we substitute 2y instead of x in one of the previous equations we will obtain...

6y + x = 8

6y + 2y = 8

8y = 8

y = 1

From the equation x = 2y we know that...

x = 2y

x = 2(1)

x = 2

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sertanlavr [38]

The solution is $x = 2 \text{ and } y = \frac{1}{2}$

Solution:

Let us assume,

$a = \frac{1}{x}\\\\b = \frac{1}{y}$

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Rewrite the equation using "a" and "b"

2a - 3b = -5 ------------ eqn 1

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Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 2

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Add eqn 2 and eqn 3

4a + 6b = 14

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Now let us go back to our assumed values

Substitute a = 1/2 in assumed values

$a = \frac{1}{x}\\\\\frac{1}{2} = \frac{1}{x}\\\\x = 2$

Substitute b = 2 in assumed value

$b = \frac{1}{y}\\\\2 = \frac{1}{y}\\\\y = \frac{1}{2}$

Thus the solution is $x = 2 \text{ and } y = \frac{1}{2}$

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Step-by-step explanation:

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