3x+2y = 24 Erica's goal is to score at least 24 points in her next playground basketball game. The given inequality represents this goal, where x is the number of 3 -point field goals she scores and y is the number of 2 -point field goals she scores. If she scores 53 -point field goals, what is the minimum number of 2-point field goals she must score to meet her scoring goal?

Question

3x+2y >= 24 Erica's goal is to score at least 24 points in her next playground basketball game. The given inequality represents this goal, where  x is the number of 3 -point field goals she scores and  y is the number of 2 -point field goals she scores. If she scores 53 -point field goals, what is the minimum number of 2-point field goals she must score to meet her scoring goal?

Bytelearn · Accepted Answer

Identify inequality and variables: Identify the given inequality and the variables. The inequality given is 3x + 2y >= 24, where x is the number of 3-point field goals and y is the number of 2-point field goals Erica scores.Substitute value of x: Substitute the value of x into the inequality. Erica scores 5 3-point field goals, so x = 5. We substitute this value into the inequality to find the minimum number of 2-point field goals (y) she needs to score. 3(5) + 2y >= 24Perform multiplication: Perform the multiplication to simplify the inequality. 3 * 5 = 15, so the inequality becomes: 15 + 2y >= 24Isolate variable y: Isolate the variable y on one side of the inequality. To find the value of y, we need to subtract 15 from both sides of the inequality. 15 + 2y - 15 >= 24 - 15 2y >= 9Divide both sides: Divide both sides of the inequality by 2 to solve for y. 2y / 2 >= 9 / 2 y >= 4.5Round up to nearest whole number: Since Erica cannot score half a field goal, we round up to the nearest whole number. Erica must score at least 5 2-point field goals to meet her scoring goal.

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