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notka56 [123]
2 years ago
5

Paint costing $19 per gallon is to be mixed with thinner costing $3 per gallon. How much of each should be added to make 16 gall

ons of a mix that costs $14 per gallon?
Mathematics
1 answer:
Evgen [1.6K]2 years ago
4 0
Let x represent gallons of $19 paint
let y represent gallons of $3 paint

first you make your 2 equations

x+y=16, y=16-x
(19x+3y) ÷ 16 = 14

then you use substitution

14 = (19x + 3(16-x) ) ÷16
224 = 19x + 48 - 3x
176 = 16x
11 = x, so there's 11 gallons of $19 paint
recall that x+y=16
11+y=16
5=y

so there are 11 gallons of $19 paint and 5 gallons of $3 paint


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Step-by-step explanation:

x

2

+

x

−

6

=

(

x

+

3

)

(

x

−

2

)

x

2

−

3

x

−

4

=

(

x

−

4

)

(

x

+

1

)

Each of the linear factors occurs precisely once, so the sign of the given rational expression will change at each of the points where one of the linear factors is zero. That is at:

x

=

−

3

,

−

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Note that when

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x

2

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Hence the sign of the value of the rational expression in each of the intervals

(

−

∞

,

−

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)

,

(

−

3

,

−

1

)

,

(

−

1

,

2

)

,

(

2

,

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)

and

(

4

,

∞

)

follows the pattern

+

−

+

−

+

. Hence the intervals

(

−

3

,

−

1

)

and

(

2

,

4

)

are both part of the solution set.

When

x

=

−

1

or

x

=

4

, the denominator is zero so the rational expression is undefined. Since the numerator is non-zero at those values, the function will have vertical asymptotes at those points (and not satisfy the inequality).

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x

=

−

3

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x

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2

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x

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[

−

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