5Question: A soil microbiologist purchases 5 units of bacterial culture X and 3 units of fungus Y for \$45.00, and 2 units of X and 4 units of Y for \$32.00. What is the cost of one unit of X in cents?

["Title: How a Soil Microbiologist Solves Pricing Puzzles: Solving the 5-X & 3-Y Cost Equation", "Soil microbiologists often juggle more than petri dishes and growth media—they also analyze complex cost structures behind laboratory supplies. One classic problem reveals how a precise mathematical approach can clarify purchasing decisions. In this case, a scientist buys five units of bacterial culture X and three units of fungal culture Y for $45.00, and two units of X and four units of Y for $32.00. Wondering what one unit of bacterial culture X costs in cents? Let’s unpack the mystery using a system of equations.", "---", "### The Problem Breakdown", "Let the price per unit of bacterial culture X be x dollars, and fungus Y be y dollars.", "From the given purchases, we form two equations:", "1. 5x + 3y = 45.00 (Equation A)\n2. 2x + 4y = 32.00 (Equation B)", "We want to find the value of x and convert it to cents (1 dollar = 100 cents).", "---", "### Step 1: Simplify the Equations", "Start with Equation A:\n5x + 3y = 45.00   (Equation A)", "And Equation B:\n2x + 4y = 32.00  (Equation B)", "To eliminate one variable, we can use the elimination method. First, make the coefficients of y equal. Multiply Equation A by 4 and Equation B by 3:", "- 4×(5x + 3y) = 4×45.00 → 20x + 12y = 180\n- 3×(2x + 4y) = 3×32.00 → 6x + 12y = 96", "Now subtract the second new equation from the first:", "(20x + 12y) − (6x + 12y) = 180 − 96\n→ 14x = 84\n→ x = 84 ÷ 14 = 6.00", "So, one unit of bacterial culture X costs $6.00.", "---", "### Step 2: Convert to Cents", "Since the question asks for the cost in cents, multiply by 100:", "6.00 dollars = 6 × 100 = 600 cents", "---", "### Why This Matters for Soil Scientists", "Accurately interpreting supply costs helps lab managers budget efficiently for research projects. Whether testing microbial interactions or conducting field studies, understanding exact pricing ensures resources are allocated wisely—especially when multiple components like X and Y are purchased in specific ratios.", "---", "### Final Answer", "The cost of one unit of bacterial culture X is 600 cents.", "---", "Key Takeaway:\nSet up linear equations from real-world purchases, solve using elimination, and convert to cents when needed. This method empowers any soil microbiologist—or cost-conscious researcher—to make informed purchasing choices.", "---", "Tags: soil microbiology, cost calculation, lab budgeting, bacterial culture X price, fungal culture Y cost, equation solving, microbiology lab expenses, soil microbiologist supplies, scientific pricing analysis"]