Question 7

Mai and Tyler are selling items to earn money for their elementary school. The school earns w dollars for every wreath sold and p dollars for every potted plant sold. Mai sells 14 wreaths and 3 potted plants and the school earns $70.50. Tyler sells 10 wreaths and 7 potted plants and the school earns $62.50.

This situation is represented by this system of equations: { 14 w + 3 p = 70 . 50 10 w + 7 p = 62 . 50

Which statements are true in explaining why it makes sense that the solution of this system is also a solution to 4 w + ( − 4 p ) = 8 . 00 ? Select all that apply. (Lesson 2-15) Multiple select question.

A) Because 10 w + 7 p is equal to 62.50, subtracting 10 w + 7 p from the left side of 14 w + 3 p = 70 . 50 and subtracting 62.50 from its right side keep the two sides equal.
B) The equation 4 w + ( − 4 p ) = 8 . 00 is the result of adding the two equations in the system and then dividing the result by 6.

C) The equation 4 w + ( − 4 p ) = 8 . 00 is the result of subtracting the second equation in the system from the first equation.

D) The equation 4 w + ( − 4 p ) = 8 . 00 represents the difference between Mai's sales and Tyler's sales, or the result of subtracting Tyler's sales from Mai's.

E) The left side of the equation 4 w + ( − 4 p ) = 8 . 00 shows the difference in terms of the items sold. The right side shows the difference in dollars. The cost per wreath, w, and the cost per potted plant, p, haven't changed.