Problem 20 - Prealgebra

Question

Juan needs to save \(\$ 125\) for a ski trip. He has \(\$ 68\) in his bank. He receives \(\$ 15\) for an allowance and earns \(\$ 20\) delivering newspapers and \(\$ 16\) shoveling snow. Does he have enough money for the trip? Explain.

Step-by-Step Solution

Answer

Juan does not have enough money; he's $6 short.

Step 1: Calculate Total Money from Allowance and Work

Add the amounts Juan receives from his allowance, newspaper delivery, and snow shoveling: \(\\(15 + \\)20 + \\(16 = \\)51\).

Step 2: Calculate Total Money Available

Add the total from Juan's bank account to his earnings: \(\\(68 + \\)51 = \$119\).

Step 3: Compare Total Savings to Trip Cost

Determine if the total money available is enough for the ski trip by comparing it with the cost of the trip: \(\\(119 < \\)125\). Juan does not have enough money.

Key Concepts

Money Management

Managing money wisely helps in achieving financial goals, whether they're short-term like a ski trip or long-term like saving for college. Good money management involves knowing exactly how much money you have, how much more you need, and how to strategize the best ways to save or earn additional funds.

For Juan, understanding his current financial situation is crucial. He starts with $68 in the bank. Each source of income such as allowance, newspaper delivery, and snow shoveling contributes to his total funds. He needs to be aware of how each amount adds up over time.

Tracking every dollar, Juan can make informed financial decisions. This can include making choices on where to cut back on spending or looking for additional ways to earn money. In this way, money management becomes a powerful tool for reaching his goals.

Problem-Solving Steps

Breaking a problem into smaller, manageable steps can simplify complex situations. Here's how this applies to Juan's situation:

• Identify All Income: List all sources of money. For Juan, this includes allowance, newspaper delivery, and snow shoveling.
• Calculate Total Earnings: Add the amounts together to know your total extra funds. Juan does this and finds his income is $51.
• Evaluate Current Savings: Add your latest total to any current savings. Juan adds his bank savings to his earnings, resulting in $119 total available.
• Make Comparisons: Compare these funds to your goal. Juan needs $125, so he discovers that he falls short.
• Decide on Next Steps: If the balance is insufficient, consider how to close the gap, such as saving more or finding additional work.

Following these problem-solving steps helps to systematically address goals and obstacles.

Comparing Numbers

Comparison of numbers is a valuable skill in both mathematics and real-world applications. When we compare numbers, we establish relationships like which is greater, lesser, or if they are equal.

This is particularly important in financial decisions, such as deciding if you have enough money for a particular need. In Juan's situation, his total funds amount to $119, but his goal is to save $125. By comparing these numbers, Juan can clearly see that $119 is less than $125.

Understanding number comparison helps identify what needs to be done next. It answers questions like, "Do I need to earn more?" or "Can I spend less in another area to reach my goal?" This skill goes beyond math classes, offering a tool for everyday decision-making and planning.