Set 3: Systems of Equations (Intermediate)

Choice A is correct. Choice A is the correct answer. Let $s$ = small coffees and $L$ = large coffees. Step 1: Set up the system: $\begin{cases} s + L = 80 \\ 3 s + 5 L = 340 \end{cases}$ Step 2: From the first equation: $L = 80 - s$ Step 3: Substitute into the second equation: $$$3s + 5(80 - s) = 3403s + 400 - 5 s = 340$-2 s = -60s = 30 Solution: 30 small coffees (and 50 large coffees) Verification: $30+ 50 = 80$ ✓ and $3(30) + 5(50) = 90 + 250 = 340$ ✓ Strategic Tip: In mixture/combination problems, one equation represents quantity, the other represents value. Choice B is incorrect because $3(40) + 5(40) = 320 \neq 340$. Choice C is incorrect because $3(50) + 5(30) = 300 \neq 340$. Choice D is incorrect because $3(20) + 5(60) = 360 \neq 340$.