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3 years ago

Solve the equation. Check for extraneous solutions.

Mathematics

1 answer:

Sliva [168]3 years ago

3 0

Assume
if |a|=b
a=b and -a=b

so

9|9-8x|=2x+3
divide both sides by 9
|9-8x|=2/9x+1/3
assume
9-8x=2/9x+1/3 and
-9+8x=2/9x+1/3

9-8x=2/9x+1/3
times 9 both sides
81-72x=2x+3
add 72x both sides
81=74x+3
minus 3
78=74x
divide both sides by 74
39/37=x

other one
-9+8x=2/9x+1/3
multiply both sides by 9
-81+72x=2x+3
minus 2x both sides
-81+70x=3
add 81 to both sides
70x=84
divide boh sides by 70
x=6/5

x=39/37 and 6/5
check

9|9-8(39/37)|=2(39/37)+3
2646/37=189/37
false

9|9-8(6/5)|=2(6/5)+3
351/5=27/5
false

no soltion evidently, weird

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You need to delete the root by ^2. First you need to leave it alone

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vesna_86 [32]

Using a system of equations, it is found that:

38% consumes vanilla.
14% consumes strawberry.
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In our system, we have that:

x is the percentage of vanilla.
y is the percentage of strawberry.
z is the percentage of chocolate.

Those 3 compromise 97% of the flavors, hence:

$x + y + z = 97$

Vanilla sells 10% more than twice strawberry, hence:

$x = 10 + 2y$

Chocolate sells 7% more than vanilla, hence:

$z = x + 7$

Since $x = 10 + 2y$

$z = 10 + 2y + 7$

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Replacing in the first equation, we can solve for y:

$x + y + z = 97$

$10 + 2y + y + 2y + 17 = 97$

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$y = \frac{70}{5}$

$y = 14$

With y, we can solve for x and for z.

$x = 10 + 2y = 10 + 2(14) = 38$

$y = 2y + 17 = 2(14) + 17 = 45$

Hence:

38% consumes vanilla.
14% consumes strawberry.
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A similar problem is given at brainly.com/question/24778333

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