william buys two bags of peaches and three bags of apricots for $17. sylvia buys four bags of peaches and…

william buys two bags of peaches and three bags of apricots for $17. sylvia buys four bags of peaches and two bags of apricots for $22 from the same store. what is the cost of one bag of peaches?\na. $3\nb. $4\nc. $5\nd. $7

william buys two bags of peaches and three bags of apricots for $17. sylvia buys four bags of peaches and two bags of apricots for $22 from the same store. what is the cost of one bag of peaches?\na. $3\nb. $4\nc. $5\nd. $7

Answer

Explanation:

Step1: Set up equations

Let the cost of one - bag of peaches be $x$ and the cost of one - bag of apricots be $y$. William's purchase gives the equation $2x + 3y=17$. Sylvia's purchase gives the equation $4x + 2y = 22$.

Step2: Manipulate the first equation

Multiply the equation $2x + 3y=17$ by 2 to get $4x+6y = 34$.

Step3: Subtract equations

Subtract the equation $4x + 2y = 22$ from $4x+6y = 34$. $(4x + 6y)-(4x + 2y)=34 - 22$. $4x+6y - 4x - 2y=12$. $4y=12$, so $y = 3$.

Step4: Substitute $y$ into the first equation

Substitute $y = 3$ into $2x+3y = 17$. $2x+3\times3=17$. $2x+9 = 17$. $2x=17 - 9=8$. $x = 4$.

Answer:

B. $4$