Question

The equation 1.5g + 3.5w = 21 represents the number of pounds of grapes and watermelon that can be purchased for

$21. Grapes cost $1.50 per pound, and watermelon slices cost $3.50 per pound.

Answer 1

The provided equation, 1.5g + 3.5w = 21, reflects a budget constraint for purchasing grapes and watermelon with a total of $21, with grapes costing $1.50 per pound and watermelon costing $3.50 per pound.

Step-by-step explanation:

Solving a Linear Equation with Two Variables

The equation provided, 1.5g + 3.5w = 21, represents a linear equation in two variables where g stands for the pounds of grapes and w stands for slices of watermelon. Since we know the price per pound for both grapes and watermelon, we can understand this equation as a budget constraint for spending exactly $21 on these fruits.

Step-by-Step Explanation

1. Identify the cost per unit: Grapes cost $1.50 per pound and watermelon slices cost $3.50 per pound.
2. Understand the equation coefficients: The coefficients 1.5 and 3.5 in the equation correspond to the cost per unit of grapes and watermelons respectively.
3. Interpret the equation: The sum of the products of the quantities of grapes and watermelons and their unit prices equals the total amount of $21.
4. Solve for one variable: To find out how many pounds of grapes or slices of watermelon one can buy, you could express one variable in terms of the other and then use the value of one 1 to solve for the other.

This equation requires knowledge of simple algebraic manipulation and understanding of linear equations with two variables, common in budgeting and cost-related problems.