🍱 Bento, mochi, and tea for three friends

A closer look at one question · SMC 2026 mock, Question 22 (bank id B7)

Hana bought 4 bento + 2 tea for $35. Ken bought 2 bento + 3 mochi + 1 tea for $35.50. Miki bought 2 bento + 1 mochi + 2 tea for $27.50. 2 mochi cost the same as 3 tea. What is the cost of 1 bento?

1 Swap every mochi for tea first

Since 2 mochi = 3 tea, one mochi is worth 1½ tea. Rewrite Ken's and Miki's orders with NO mochi left in them:

	order	cost
Ken	2 bento + 5½ tea (3 mochi → 4½ tea, + 1 tea)	$35.50
Miki	2 bento + 3½ tea (1 mochi → 1½ tea, + 2 tea)	$27.50

2 Both now have 2 bento — so SUBTRACT to cancel them

Ken − Miki

2 tea = 35.50 − 27.50 = $8

So 1 tea = $4.

3 Put the tea price back into Miki's order

Miki

2 bento3½ tea = $14

2 bento = 27.50 − 14 = $13.50, so 1 bento = $6.75.

$6.75

per bento. (Check with Hana: 4 × 6.75 + 2 × 4 = 27 + 8 = $35 ✓)

The trap: starting from Hana's line. Ken's and Miki's lines both contain 2 bento sets, so subtracting THOSE two removes the bento and leaves only tea — choosing which two lines to subtract is the whole trick.