A gym charges a one-time registration fee as well as a monthly fee. The cost of joining the gym for 4 months is $370, and the co

st of joining for 6 months is$530. Write and solve a system of equations to find the registration fee and monthly fee.

Mathematics

1 answer:

Anna007 [38]3 years ago

8 0

$x-\ registration\ fee\\
y-\ monthly\ fee\\\\
 \left \{ {{x+4y=370} \atop {x+6y=530\ \ |*(-1)}} \right. \\\\
 \left \{ {{x+4y=370} \atop {-x-6y=-530}} \right. \\+-----\\Addition\\\\
-2y=-160\ \ | divide\ by\ -2\\
y=80\\\\
x=370-4y=370-4*80=370-320=50\\\\
Registration\ fee\ is\ equal\ to\ 50\$\ and\ monthly\ fee\ is\ equal\ to\ 80\$.
$

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Find all constants a such that the vectors (a, 4) and (2, 5) are parallel.

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Answer:

$\displaystyle a = \frac{8}{5}$ .

Step-by-step explanation:

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$\displaystyle \frac{x_1}{x_2} = \frac{y_1}{y_2}$ .

Equivalently:

$\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}$ .

For the two vectors in this equation to be parallel to one another:

$\displaystyle \frac{a}{4} = \frac{2}{5}$ .

Solve for $a$ :

$\displaystyle a = \frac{8}{5}$ .

$\displaystyle \frac{8}{5}$ would be the only valid value of $a$ ; no other value would satisfy the $\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}$ equation.