A park has a grinkgo tree a dogwood tree and 2 blue spruce trees the blue spruce trees are 8 years old the grinkgo tree is 2 years less than three times the age of the dogwood tree the grinkgo tree is also half the sum of the ages of the dogwood tree and both if the blue spruce trees write and solve an equation to find the ages of the grinkgo and the dogwood trees.

Answer:The age of the grinkgo tree is 10 years old and the age of the dogwood tree is 4 years old Step-by-step explanation:Let x -----> the age of the grinkgo treey -----> the age of the dogwood treez -----> the age of the blue spruce treewe know that[tex]x=3y-2[/tex] ------> equation A[tex]z=8[/tex] ----> equation B[tex]x=\frac{1}{2}(y+2z)[/tex]substitute the value of z[tex]x=\frac{1}{2}(y+2(8))[/tex][tex]x=\frac{1}{2}(y+16)[/tex] -----> equation Cequate equation A and equation C and solve for y[tex]3y-2=\frac{1}{2}(y+16)\\6y-4=(y+16)\\6y-y=16+4\\5y=20\\y=4[/tex]Find the value of x (equation A or equation C)[tex]x=3(4)-2=10[/tex] thereforeThe age of the grinkgo tree is 10 years old and the age of the dogwood tree is 4 years old