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solmaris [256]
3 years ago
12

Sam wants to buy 8 pencils and 6 pens, which cost a total of $8.50. He realizes he doesn't have enough cash and instead takes on

ly 4 of each, which costs only $5. What is the price of each pen and pencil? pen, $0.75; pencil, $0.50
Mathematics
1 answer:
Diano4ka-milaya [45]3 years ago
8 0
X = pencils, y = pens

8x + 6y = 8.50
4x + 4y = 5.....multiply by -2
----------------
8x + 6y = 8.50
-8x - 8y = -10 (result of multiplying by -2)
-----------------add
-2y = - 1.50
y = -1.50 / -2
y = 0.75 <=== pens cost 0.75

4x + 4y = 5
4x + 4(0.75) = 5
4x + 3 = 5
4x = 5 - 3
4x = 2
x = 2/4
x = 0.50 <== pencils cost 0.50
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What 2 numbers multiply to be -14 and add to be -3
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Xy = -14
x + y = -3

xy = -14
\frac{xy}{x} = \frac{-14}{x}
y = \frac{-14}{x}

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x^{2} + 3x - 14 = 0
x = \frac{-(3) \± \sqrt{(3)^{2} - 4(1)(-14)}}{2(1)}
x = \frac{-3 \± \sqrt{9 + 56}}{2}
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x = \frac{-3 \± 8.06}{2}
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x = -1.5 + 4.03    or    x = -1.5 - 4.03
x = 2.53    or    x = -5.53

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 - 2.53         - 2.53
              y = -5.53
        (x, y) = (2.53, -5.53)
         
         x + y = -3
  -5.53 + y = -3
+ 5.53         + 5.53
              y = 2.53
        (x, y) = (-5.53, 2.53)

The two numbers that multiply to -14 and add up to -3 are -5.53 and 2.53.
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Please help!!!!!!!!!!!!!!!!!!!!!
sleet_krkn [62]
It would be c I think
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