Question
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Michelle bought a bunch of balloons and three letters for \( \$ 5.75 \). Jesus bought two bunches of balloons and two letters for \( \$ 7.50 \).

Ask by Cook Carroll. in the United States
Feb 13,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

A bunch of balloons costs $2.75, and a letter costs $1.00.

Solution

Let B be the price of a bunch of balloons and L be the price of one letter. Michelle’s purchase gives us:   B + 3L = 5.75 Jesus’s purchase gives:   2B + 2L = 7.50 Step 1: Simplify Jesus’s equation by dividing both sides by 2:   B + L = 3.75 Step 2: Subtract the simplified equation (B + L = 3.75) from Michelle’s equation (B + 3L = 5.75):   (B + 3L) − (B + L) = 5.75 − 3.75   The B’s cancel, and we have:   2L = 2 Step 3: Solve for L:   L = 2 / 2 = 1.00 Step 4: Substitute L back into B + L = 3.75:   B + 1.00 = 3.75   B = 3.75 − 1.00 = 2.75 Answer:   A bunch of balloons costs $2.75, and a letter costs $1.00.

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The Deep Dive

Let’s break down the mystery of balloons and letters! Michelle’s purchase can be represented with the equation \( b + 3l = 5.75 \), where \( b \) is the cost of one bunch of balloons and \( l \) is the cost of one letter. Meanwhile, Jesus’s equation is \( 2b + 2l = 7.50 \). By simplifying the second equation to \( b + l = 3.75 \), we can substitute to find the price of each item. Fun, right? Once you solve the equations, you discover that one bunch of balloons costs \( \$2.00 \) and each letter costs \( \$1.75 \). This scenario is a classic example of using systems of equations to solve real-life pricing problems, which is super handy for budgeting your next birthday party! Keep those equations handy for any shopping mystery!

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