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Study Guides > Prealgebra

Putting It Together: Real Numbers

Remember Jose, the treasurer of the Aspiring Entrepreneurs Club? We left him standing in the grocery store aisle, puzzling over how many bags of chips and packages of cookies to buy for the party he was planning. Let's review what we know before we apply what you've learned to solve the problem:
  • Jose has a budget of [latex]$76[/latex].
  • A bag of chips costs [latex]$3[/latex].
  • A package of cookies costs [latex]$2[/latex].
  • A 12-pack of soda costs [latex]$5[/latex].
  • Jose needs to buy five packs of soda.
  • Jose wants to buy two more bags of chips than packages of cookies.
Let's start by setting up our equation. We know we're going to add together three amounts to get the total cost of snacks and drinks for the party: the cost of chips, the cost of cookies, and the cost of drinks. Next, let's plug in the numbers that we know. Jose is going to buy five 12-packs of soda, and each of them costs [latex]$5[/latex]. So we can write the cost of soda like this: [latex-display]5(5)[/latex-display] But what about the costs of chips and cookies? If we let the number of packages of cookies equal [latex]x[/latex], we can write the number of packages of chips as [latex]x+2[/latex]. Then we need to multiply by the price of each: Cost of cookies: [latex]2x[/latex] Cost of chips: [latex]3(x+2)[/latex] Now we can set up our equation: [latex-display]3(x+2)+2x+5(5)=76[/latex-display] Let's use the Distributive Property to remove the parentheses: [latex-display]3(x+2)=3x+6[/latex-display] [latex-display]3x+6+2x+5(5)=76[/latex-display] We can also simplify the cost of the soda by multiplying: [latex-display]5\cdot 5=25[/latex-display] Plug that into the equation: [latex-display]3x+6+2x+25=76[/latex-display] Now we can use the Commutative Property of Addition to combine like terms and simplify: [latex-display]3x+2x+6+25=76[/latex-display] [latex-display]5x+31=76[/latex-display] With both sides of the expression simplified, we can use the Subtraction Property of Equality. Subtract [latex]31[/latex] from both sides [latex-display]5x+31-31=76-31[/latex-display] [latex-display]5x=45[/latex-display] Finally, we can use the Division Property of Equality to divide both sides by [latex]5[/latex] and solve for [latex]x[/latex]: [latex-display]\frac{5x}{5}=\frac{45}{5}[/latex-display] [latex-display]x=9[/latex-display] Jose can buy [latex]9[/latex] packages of cookies. Remember that he wants to buy two more bags of chips than packages of cookies, so that equals [latex]11[/latex] bags of chips. Thanks to Jose, the refreshments at the Aspiring Entrepreneurs Club's party will be plentiful and within budget! Are you excited to try applying some math when planning your next party?

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