Question

lesson 12: writing and graphing systems of linear equations

• lets recall what it means to solve a system of linear equations and how to do it by graphing.

12.1: math talk: a possible mix?
diego bought some raisins and walnuts to make trail mix.
raisins cost $4 a pound and walnuts cost $8 a pound.
diego spent $15 on both ingredients.
decide if each pair of values could be a combination of raisins and walnuts that diego bought.
4 pounds of raisins and 2 pounds of walnuts
1 pound of raisins and 1.5 pounds of walnuts
2.25 pounds of raisins and 0.75 pounds of walnuts
3.5 pounds of raisins and 1 pound of walnuts

Explanation:

Step1: Set up cost - equation

Let $x$ be the pounds of raisins and $y$ be the pounds of walnuts. The cost equation is $4x + 8y=15$.

Step2: Check first pair

For $x = 4$ and $y = 2$, substitute into the equation: $4\times4+8\times2=16 + 16=32
eq15$.

Step3: Check second pair

For $x = 1$ and $y = 1.5$, substitute: $4\times1+8\times1.5=4 + 12=16
eq15$.

Step4: Check third pair

For $x = 2.25$ and $y = 0.75$, substitute: $4\times2.25+8\times0.75=9 + 6=15$.

Step5: Check fourth pair

For $x = 3.5$ and $y = 1$, substitute: $4\times3.5+8\times1=14 + 8=22
eq15$.

Answer:

The combination of 2.25 pounds of raisins and 0.75 pounds of walnuts is the only one that Diego could have bought.