Question 515·Easy·Algebra

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A juice bar sells smoothies for $4 each and juices for $3 each. A customer has at most $24 to spend on these drinks. Which inequality represents this situation, where $s$ is the number of smoothies and $j$ is the number of juices the customer can buy?

A spending limit calls for a budget inequality, a comparison between total cost and money available. Multiply each item's price by its count, then add the costs. Match each price to the right item before choosing a symbol. At most includes spending the entire budget, so a strict $<$ would rule out a valid purchase.

Hints

Hint 1
A cost term is the price of one item multiplied by its count. Pair each drink's price with the variable for that drink, then add the terms to get the total cost.
Hint 2
A maximum is an upper limit, not an amount you must spend. With an at-most limit, can you spend exactly that amount? Let that decide between $<$ and $\le$ .

Step-by-step

Build the budget inequality
Step 1
Write the total cost
No Desmos needed. You're translating a budget, not solving an equation. Each smoothie costs $4, so $s$ smoothies cost $4s$ . Each juice costs $3, so $j$ juices cost $3j$ . Add these cost terms to get the total cost, $4s+3j$ .
Step 2
Apply the spending limit
At most means less than or equal to, including the limit itself. So the budget inequality is $4s+3j\le24$ . The customer can buy combinations costing no more than $24, including exactly $24. Choice C.

Question 515·Easy·Algebra

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