Answer:
$4500
Step-by-step explanation:
Strategy
Joe's requirement for hotel rooms includes the rooms he has booked plus some extra, bringing the total to at least 50. This can be expressed through an inequality that resembles the following:
\left( \text{reserved rooms} \right) + \left( \text{extra rooms} \right) [\leq \text{or} \geq] \,50(rooms reserved)+(extra rooms)[≤or≥]50left parenthesis, start text, r, e, s, e, r, v, e, d, space, r, o, o, m, s, end text, right parenthesis, plus, left parenthesis, start text, e, x, t, r, a, space, r, o, o, m, s, end text, right parenthesis, open bracket, is less than or equal to, start text, o, r, end text, is greater than or equal to, close bracket, 50
Now, we can solve this inequality to determine the number of additional blocks Joe needs to secure.
Hint #22 / 4
1) Which inequality?
Joe has already made a reservation and payment for \blueD{16}16start color #11accd, 16, end color #11accd rooms.
Each block consists of 888 rooms, with BBB denoting the number of extra blocks, thus the additional rooms from these blocks equate to \greenD{8B}8Bstart color #1fab54, 8, B, end color #1fab54.
The total number of rooms reserved plus the extra must amount to \maroonD{\text{greater than or equal to }} 50greater than or equal to 50start color #ca337c, start text, g, r, e, a, t, e, r, space, t, h, a, n, space, o, r, space, e, q, u, a, l, space, t, o, space, end text, end color #ca337c, 50 rooms.
\begin{aligned} \left( \blueD{\text{reserved rooms}} \right) &+ \left( \greenD{\text{extra rooms}} \right) [\leq \text{or} \geq] \,50 \\\\ \blueD{16}&+\greenD{8B} \maroonD{\geq} 50 \end{aligned}
(reserved rooms)
16
+(extra rooms)[≤or≥]50
+8B≥50
Hint #33 / 4
2) How many additional blocks must Joe reserve?
Now, let’s solve the inequality for BBB:
16+8B
8B
B
≥50
≥34
≥4.25
Remove 16
Divide by 8
Since partial blocks cannot be booked, Joe needs 555 extra blocks. Each block incurs a fee of \$900$900dollar sign, 900, so acquiring 555 new blocks will total 5 \cdot \$900=\$45005⋅$900=$45005, dot, dollar sign, 900, equals, dollar sign, 4500.
[Let’s verify the solution]
Hint #44 / 4
Answers
1) The established inequality is
16+8B \geq 5016+8B≥5016, plus, 8, B, is greater than or equal to, 50
2) Joe's expenditure on extra rooms amounts to \$4500$4500dollar sign, $4500.
