Question

There are 80 major sources of pollen in state A. These pollen sources are categorized as​ grasses, weeds, and trees. If the number of weeds is 7 less than thrice the number of​ grasses, and the number of trees is 3 more than thrice the number of​ grasses, find the number of​ grasses, weeds, and trees that are major pollen sources.

Answer 1

Answer:

Grasses: 12

Weeds: 29

Trees: 39

Step-by-step explanation:

Let G, W and T represent number of grasses, weeds, and trees that are major pollen sources.

We have been given that there are 80 major sources of pollen in state A. We can represent this information in an equation as:

$G+W+T=80...(1)$

We are told that the number of weeds is 7 less than thrice the number of​ grasses. We can represent this information in an equation as:

$W=3G-7...(2)$

We are also told that the number of trees is 3 more than thrice the number of​ grasses. We can represent this information in an equation as:

$T=3G+3...(3)$

Upon substituting equation (2) and equation (3) in equation (1), we will get:

$G+3G-7+3G+3=80$

$7G-4=80$

$7G-4+4=80+4$

$7G=84$

$\frac{7G}{7}=\frac{84}{7}$

$G=12$

Therefore, there are 12 grasses that are major pollen sources.

Number of weeds that are major pollen sources:

$W=3G-7\Rightarrow 3(12)-7=36-7=29$

Therefore, there are 29 weeds that are major pollen sources.

Number of trees that are major pollen sources:

$T=3G+3\Rightarrow 3(12)+3=36+3=39$

Therefore, there are 39 trees that are major pollen sources.