There are 53 major sources of pollen in state A. These pollen sources are categorized as grasses, weeds, and trees. If the number of weeds is 9 less than twice the number of grasses, and the number of trees is 2 more than twice the number of grasses, find the number of grasses, weeds, and trees that are major pollen sources. The number of grasses in state A is .

Let's denote the number of grasses as \( g \). According to the problem, the number of weeds can be expressed as \( 2g - 9 \), and the number of trees can be expressed as \( 2g + 2 \). We know the total number of pollen sources equals 53: \[ g + (2g - 9) + (2g + 2) = 53 \] Combining like terms gives us: \[ 5g - 7 = 53 \] Adding 7 to both sides: \[ 5g = 60 \] Thus, dividing by 5: \[ g = 12 \] So, the number of grasses in state A is 12. Using \( g = 12 \): - Weeds: \( 2(12) - 9 = 24 - 9 = 15 \) - Trees: \( 2(12) + 2 = 24 + 2 = 26 \) To summarize: - Grasses: 12 - Weeds: 15 - Trees: 26 And indeed, \( 12 + 15 + 26 = 53 \).