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3 years ago

HELP, PLEASE.

1 answer:

6 0

X=amount of apples bought. (in pounds)
y=amount of bananas boutht (in pounds)
We can suggest this system of equations:

x+y=3.8
1.9x+0.75y=5.84

We can solve this system of euqtions by substitution method.
x+y=3.8 ⇒ y=3.8-x

1.9x+0.75(3.8-x)=5.84
1.9x+2.85-0.75x=5.85
1.15x=5.84-2.85
1.15x=2.99
x=2.99/1.15
x=2.6

y=3.8-x
y=3.8-2.6
y=1.2

Answer: C. 2.6 pounds of apples; 1.2 pounds of bananas.

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We are to find the co-ordinates of point C that sit 3/8 of the way along AB, where the point P is close to A than to B.

According to the given information, we have

$\dfrac{AC}{AB}=\dfrac{3}{8}\\\\\Rightarrow \dfrac{AC}{AC+BC}=\dfrac{3}{8}\\\\\Rightarrow 8AC=3AC+3BC\\\\\Rightarrow 5AC=3BC\\\\\Rightarrow AC:BC=3:5.$

So, point C divides the line segment AB in the ratio 3 : 5.

We know that

if a point Q divides a line segment joining the points S(a,b) and T(c,d), in the ratio m : n, then the co-ordinates of Q are

$\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).$

Therefore, the co-ordinates of point C are

$\left(\dfrac{3\times19+5\times3}{3+5},\dfrac{3\times(-1)+5\times(-5)}{3+5}\right)\\\\\\=\left(\dfrac{57+15}{8},\dfrac{-3-25}{8}\right)\\\\=(9,-3.5).$

Thus, the required co-ordinates of point C are (9, -3.5).

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