Addison paid $10 for 2 granola bars and 6 apples. George paid $7 for 2 granola bars and 3 apples. Find the cost of each granola bar and each apple.

Answer:g(granola bar) = $2 and a(apple) = $1Step-by-step explanation:This problem can be modeling as an equation systems with two unknows. We can writting the equation systems as follows:For Addison [tex]2g+6a=10[/tex] where "g" is a granola bar price, "a" an apple price, and 10 is the sum of both product prices in dollars. For George [tex]2g+3a=7[/tex] where "g" is a granola bar price, "a" an apple price, and 7 is the sum of both product prices in dollars. Ordering both equations:[tex]\left \{ {{2g+6a=10} \atop {2g+3a=7}} \right.[/tex]We're going to use the reduction method to solve this system of equations.The reduction method consists of adding (or subtracting) the system equations to eliminate one of the unknowns.1.  Make sure that adding or subtracting the equations, some of the unknowns disappears.We can see if we substracting both equations, the "g" unknown disappears.[tex]\left \{ {{2g+6a=10} \atop {-(2g+3a)=-(7)}} \right.[/tex][tex]\left \{ {{2g+6a=10} \atop {-2g-3a=-7}} \right.[/tex]Sustracting both equations, we obtain:[tex]0g+3a=3[/tex][tex]3a=3[/tex][tex]a=\frac{3}{3} =1[/tex] which means that the value of an apple is $1.2. We calculate the other unknown by substituting the value obtained from "a".Substituting the value from "a" in the first equation:[tex]2g+6(1)=10[/tex][tex]2g+6=10[/tex][tex]2g=10-6[/tex][tex]g=\frac{10-6}{2}[/tex][tex]g=\frac{4}{2}[/tex][tex]g=2[/tex] which means that the value of  a granola bar is $2.3. Finally, we verify the result by substituting the values ​​obtained for "g" and "a" to see if it satisfy the equations.For the first equation:[tex]2g+6a=10[/tex] with g = 2 and a = 1[tex]2(2)+6(1)=10[/tex][tex]4+6=10[/tex] For the second equation:[tex]2g+3a=7[/tex] with g = 2 and a = 1[tex]2(2)+3(1)=7[/tex][tex]4+3=7[/tex]