Toby and Janine are shopping for a king-size bed and a double bed, whose regular prices do not vary from store to store. At the first store they visit, the two beds cost a total of $1,900, as the price of the king-size bed has been reduced by 30%. At the second store they visit, the two beds cost a total of $2,010, as the price of the double bed has been reduced by 40%. If Toby and Janine buy each bed at the store where it is cheaper, how much will they pay in total?
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This one took me way longer than it should have. The trick is realizing store 1's total is king discounted + double full, and store 2 is double discounted + king full. Setting up the two equations is fine, but I kept second-guessing which bed to buy where.
Same here. Once I labeled original prices K and D it clicked, but the wording had me rereading it three times.
Yeah the 'each bed at the store where it is cheaper' part is what tests you, not the algebra.
Wait, do we compare the discounted king price at store 1 to the FULL king price at store 2? That feels like a trap because at store 2 the king isn't on sale at all.
That's exactly the point. You compare what each store actually charges for each bed, not both at sale prices. Store 1 wins on the king, store 2 wins on the double.
Got 1690 after solving. For anyone stuck: let the king be K and double be D, write 0.7K + D = 1900 and K + 0.6D = 2010. Solve, then pick the lower price for each bed separately.
Clean setup. I did the same but plugged into choices for the final total instead of computing each bed's price directly.
Hardest 700+ percentages question I've seen in a while. Respect to anyone who nailed it under two minutes.
Took me almost four minutes, so don't feel bad.
What it tests
Your ability to compute percentage change, percentage of a whole, and to work backwards from a final value.
Common trap
Treating successive percentage changes as additive — a 10% rise then a 10% fall is not back to the start.