Question 235·Medium·Algebra

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A food truck plans to prepare $x$ burritos and $y$ tacos for lunch.

Each burrito takes $3$ minutes to prepare, and each taco takes $2$ minutes.
The truck has at most $180$ minutes of prep time.
The truck wants to prepare at least $60$ total items.

Which ordered pair $(x,y)$ satisfies both conditions?

For linear-inequality word problems with two variables, translate each condition into an inequality, then test the answer choices by substitution. The correct ordered pair must satisfy every inequality at the same time.

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Turn words into inequalities

Write one inequality for the time limit and another inequality for the minimum total number of items.

Use substitution

For each answer choice, substitute its $x$ and $y$ values into both inequalities.

Both conditions must be true

Eliminate any option that fails either inequality, even if it satisfies the other one.

Desmos Guide

Enter the inequalities

In Desmos, enter $3x+2y\le 180$ and $x+y\ge 60$ .

(Optional) Restrict to realistic values

If desired, also enter $x\ge 0$ and $y\ge 0$ since numbers of items can’t be negative.

Check the answer choices as points

Plot each answer choice as a point (for example, type $(40,20)$ ). The correct choice is the only point that lies in the overlap of the shaded regions.

Step-by-step Explanation

Write the inequalities

Prep-time limit: $3x+2y\le 180$ .

Minimum number of items: $x+y\ge 60$ .

Test each ordered pair

Check each choice in both inequalities:

$(40,20)$ : $3(40)+2(20)=160\le 180$ and $40+20=60\ge 60$ (works)
$(50,20)$ : $3(50)+2(20)=190>180$ (fails)
$(30,25)$ : $30+25=55<60$ (fails)
$(20,70)$ : $3(20)+2(70)=200>180$ (fails)

Select the pair that satisfies both

Therefore, the ordered pair that satisfies both conditions is $(40,20)$ .

Question 235·Medium·Algebra

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation