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1234Linear equations

Solutions to the exercises

Exercise 1

$P = 2, 5 s - 400$

$2, 5 s - 400 = 0$ gives you $s = 160$

$2, 5 s - 400 = 1000$ gives you $s = 560$ , so more than $560$ tickets sold.

Exercise 2

$p = 12 - 0, 12 x$ and $q = 2 + 0, 1 x$
$12 - 0, 12 x = 2 + 0, 1 x$ gives you $x = 45, 454545 ...$ , so the solution of the inequality is $x \geq 45, 46$ .

Exercise 3

$C = 2, 25 + 0, 75 m$

$2, 25 + 0, 75 m = 6$ gives you $m = 5$ , so after more than $5$ minutes.

At a speed of $60$ km/h the journey would take $10$ minutes, so a rail-taxi would be cheaper.

Exercise 4

$k = 3$

$x \leq - 4$

$t > 3, 75$

$a \leq 5166 \frac{2}{3}$

multiply both sides by $20$ to get $24 - 8 x = 20 - 5 x$ and therefore $x = \frac{4}{3}$

work out the brackets to get $120 + x = 4 x + 60$ and therefore $x = 20$

Exercise 5

$T R = 10 q$ and $T C = 6, 5 q + 83000$

Calculator: Y1=10X and Y2=6.5X+83000 with settings: $0 \leq x \leq 30000$ and $0 \leq y \leq 300000$
You find: $x \approx 23714, 3$

$10 q = 6, 5 q + 83000$ gives you $q \approx 23714, 3$

When $q > 23714$

Exercise 6

$C = 1600 + 3 v$

$R = 5 v$

$5 v = 1600 + 3 v$ gives you $v = 800$ , so profit is made with more than $800$ vases sold.

$P = R - C = 5 v - (1600 + 3 v) = 2 v - 1600 = 2000$ when $v = 1800$

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