Question

1. steven has $2,500 to spend on remodeling his living room. he did some research and found the following prices for the items he wants. steven lives in a state with no sales tax so he does not have to consider the tax.

sofa $976.50
loveseat $747.50
2 chairs $490
recliner $499
lamp set $150
bookshelf $500
accent table $300
which of the following combinations can steven purchase within his budget? select all that apply.
□ sofa, loveseat, recliner, and lamp set
□ sofa, 2 chairs, lamp set, bookshelf, and accent table
□ sofa, loveseat, bookshelf, and accent table
□ sofa, 2 chairs, recliner, bookshelf, and accent table

Explanation:

Step1: Calculate total for first combination (sofa, loveseat, recliner, lamp set)

Sum their prices: $976.50 + 747.50 + 499 + 150$
$= 976.50 + 747.50 = 1724$; $1724 + 499 = 2223$; $2223 + 150 = 2373$
Since $2373 \leq 2500$, this combination is valid.

Step2: Calculate total for second combination (sofa, 2 chairs, lamp set, bookshelf, accent table)

Sum their prices: $976.50 + 490 + 150 + 500 + 300$
$= 976.50 + 490 = 1466.5$; $1466.5 + 150 = 1616.5$; $1616.5 + 500 = 2116.5$; $2116.5 + 300 = 2416.5$
Since $2416.5 \leq 2500$, this combination is valid.

Step3: Calculate total for third combination (sofa, loveseat, bookshelf, accent table)

Sum their prices: $976.50 + 747.50 + 500 + 300$
$= 976.50 + 747.50 = 1724$; $1724 + 500 = 2224$; $2224 + 300 = 2524$
Since $2524 > 2500$, this combination is invalid.

Step4: Calculate total for fourth combination (sofa, 2 chairs, recliner, bookshelf, accent table)

Sum their prices: $976.50 + 490 + 499 + 500 + 300$
$= 976.50 + 490 = 1466.5$; $1466.5 + 499 = 1965.5$; $1965.5 + 500 = 2465.5$; $2465.5 + 300 = 2765.5$
Since $2765.5 > 2500$, this combination is invalid. Wait, correction: Wait, let's recalculate this step. Wait, maybe I made a mistake. Wait, no, let's re - add: 976.50 + 490 = 1466.5; 1466.5+499 = 1965.5; 1965.5 + 500 = 2465.5; 2465.5+300 = 2765.5? Wait, no, that's wrong. Wait, 976.50 (sofa) + 490 (2 chairs) = 1466.5; +499 (recliner) = 1965.5; +500 (bookshelf) = 2465.5; +300 (accent table) = 2765.5. But 2765.5 > 2500, so this is invalid. Wait, but wait, maybe I miscalculated the third combination. Wait, sofa ($976.50$) + loveseat ($747.50$) + bookshelf ($500$) + accent table ($300$). Let's add again: 976.50 + 747.50 = 1724; 1724+500 = 2224; 2224 + 300 = 2524. 2524>2500, so invalid. Wait, but let's check the second combination again: 976.50 (sofa) + 490 (2 chairs) + 150 (lamp set) + 500 (bookshelf) + 300 (accent table). 976.50+490 = 1466.5; +150 = 1616.5; +500 = 2116.5; +300 = 2416.5. 2416.5 ≤2500, valid. Wait, and the first combination: 976.50 + 747.50 + 499 + 150. 976.50+747.50 = 1724; +499 = 2223; +150 = 2373. 2373 ≤2500, valid. Wait, also, let's check another possible combination. Wait, the third option: sofa, loveseat, bookshelf, accent table. 976.50+747.50 = 1724; +500 = 2224; +300 = 2524. 2524>2500, so invalid. Wait, but wait, maybe I missed a combination. Wait, the problem has four options:

1. sofa, loveseat, recliner, and lamp set: total $2373$ (valid)
2. sofa, 2 chairs, lamp set, bookshelf, and accent table: total $2416.5$ (valid)
3. sofa, loveseat, bookshelf, and accent table: total $2524$ (invalid)
4. sofa, 2 chairs, recliner, bookshelf, and accent table: total $2765.5$ (invalid)

Wait, but wait, maybe I made a mistake in the fourth combination. Wait, no, let's re - calculate the fourth: 976.50 (sofa) + 490 (2 chairs) + 499 (recliner) + 500 (bookshelf) + 300 (accent table). 976.50+490 = 1466.5; +499 = 1965.5; +500 = 2465.5; +300 = 2765.5. Yes, that's correct. So the valid combinations are the first and the second. Wait, but wait, let's check the third option again. Wait, sofa ($976.5$) + loveseat ($747.5$) + bookshelf ($500$) + accent table ($300$). 976.5 + 747.5 = 1724; 1724+500 = 2224; 2224 + 300 = 2524. 2524>2500, so invalid. Wait, but maybe I made a mistake in the first combination. Let's check again: sofa ($976.5$) + loveseat ($747.5$) + recliner ($499$) + lamp set ($150$). 976.5+747.5 = 1724; 1724+499 = 2223; 2223+150 = 2373. 2373 ≤2500, valid. Second combination: sofa ($976.5$) + 2 chairs ($490$) + lamp set ($150$) + bookshelf ($500$) + accent table ($300$). 976.5+490 = 1466.5; +150 = 1616.5; +500 = 2116.5; +300 = 2416.5. 2416.5 ≤2500, valid. Wait, but the problem says "select all that apply". So the valid ones are:

- sofa, loveseat, recliner, and lamp set
- sofa, 2 chairs, lamp set, bookshelf, and accent table

Wait, but let's check another possible combination. Wait, is there a third? Wait, no, the third option (sofa, loveseat, bookshelf, accent table) totals 2524 which is over 2500. The fourth option totals 2765.5 which is over. So the two valid ones are the first and the second.

Answer:

• sofa, loveseat, recliner, and lamp set
• sofa, 2 chairs, lamp set, bookshelf, and accent table