Answer:
$4500
Step-by-step explanation:
Strategy
Joe needs the rooms he's already reserved plus the additional rooms to be at least 505050. We can represent this with an inequality whose structure looks something like this:
\left( \text{rooms already reserved} \right) + \left( \text{additional rooms} \right) [\leq \text{or} \geq] \,50(rooms already reserved)+(additional rooms)[≤or≥]50left parenthesis, start text, r, o, o, m, s, space, a, l, r, e, a, d, y, space, r, e, s, e, r, v, e, d, end text, right parenthesis, plus, left parenthesis, start text, a, d, d, i, t, i, o, n, a, l, 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
Then, we can solve the inequality for BBB to find how many additional blocks Joe needs to reserve.
Hint #22 / 4
1) Which inequality?
Joe has already reserved and paid for \blueD{16}16start color #11accd, 16, end color #11accd rooms.
Each blocks has 888 rooms, and BBB represents the number of additional blocks, so the number of additional rooms from these blocks is \greenD{8B}8Bstart color #1fab54, 8, B, end color #1fab54.
The number of rooms he's already reserved plus the additional rooms needs to be \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{rooms already reserved}} \right) &+ \left( \greenD{\text{additional rooms}} \right) [\leq \text{or} \geq] \,50 \\\\ \blueD{16}&+\greenD{8B} \maroonD{\geq} 50 \end{aligned}
(rooms already reserved)
16
+(additional rooms)[≤or≥]50
+8B≥50
Hint #33 / 4
2) How many additional blocks does Joe need?
Let's solve our inequality for BBB:
16+8B
8B
B
≥50
≥34
≥4.25
Subtract 16
Divide by 8
Since he can't reserve partial blocks, Joe needs to reserve 555 additional blocks. And each block costs \$900$900dollar sign, 900, so buying 555 additional blocks costs 5 \cdot \$900=\$45005⋅$900=$45005, dot, dollar sign, 900, equals, dollar sign, 4500.
[Let's check our solution]
Hint #44 / 4
Answers
1) The inequality that describes this scenario is
16+8B \geq 5016+8B≥5016, plus, 8, B, is greater than or equal to, 50
2) Joe needs to spend \$4500$4500dollar sign, $4500 on additional rooms.
