A café sells small cold brew coffees for \4 each and large cold brew coffees for \6 each. … — GMAT

A café sells small cold brew coffees for $\$4$ each and large cold brew coffees for $\$6$ each. On Monday morning, the café sold a total of $40$ cold brew coffees for $\$196$ . How many large cold brew coffees were sold?

Answer: 18

Answer

The café sold 18 large cold brew coffees.

Setting up the system

s + l = 40

and

4s + 6l = 196

, substituting

s = 40 - l

yields

4(40 - l) + 6l = 196

. Simplifying gives

160 + 2l = 196

, so

2l = 36

and

l = 18

Step-by-Step Solution

Set up equations based on total count and total cost.

Let

s

= number of small coffees and

l

= number of large coffees. The system is

s + l = 40

and

4s + 6l = 196

The problem gives two distinct relationships between the quantity sold and the total dollar value.

Substitute

s = 40 - l

into the second equation.

4(40 - l) + 6l = 196 \implies 160 + 2l = 196

Substituting reduces the system from two variables to a single equation in

l

Solve the linear equation for

l

2l = 36 \implies l = 18

Subtracting 160 from both sides and dividing by 2 yields the number of large cold brews.

Key Concept

Solving systems of linear equations in two variables using substitution.

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