a grocery store is packaging a 150 - pound quantity of its special rice blend, which costs $4.95 per pound…

a grocery store is packaging a 150 - pound quantity of its special rice blend, which costs $4.95 per pound to make. it is made up of wild rice at $6.45 per pound and long grain brown rice at $3.95 per pound. how many pounds of each should be used to make the blend? write your answers as whole numbers or as decimals rounded to the nearest tenth. pounds of wild rice pounds of long grain brown rice

a grocery store is packaging a 150 - pound quantity of its special rice blend, which costs $4.95 per pound to make. it is made up of wild rice at $6.45 per pound and long grain brown rice at $3.95 per pound. how many pounds of each should be used to make the blend? write your answers as whole numbers or as decimals rounded to the nearest tenth. pounds of wild rice pounds of long grain brown rice

Answer

Explanation:

Step1: Set up variables

Let $x$ be the pounds of wild - rice and $y$ be the pounds of long - grain brown rice. We know two equations: $x + y=150$ (total weight) and $6.45x + 3.95y=4.95\times150$ (total cost). From $x + y=150$, we get $y = 150 - x$.

Step2: Substitute $y$ into cost equation

Substitute $y = 150 - x$ into $6.45x+3.95y = 4.95\times150$. $6.45x+3.95(150 - x)=4.95\times150$. Expand: $6.45x+592.5-3.95x = 742.5$. Combine like - terms: $(6.45x - 3.95x)+592.5 = 742.5$. $2.5x+592.5 = 742.5$.

Step3: Solve for $x$

Subtract 592.5 from both sides: $2.5x=742.5 - 592.5$. $2.5x = 150$. Divide both sides by 2.5: $x=\frac{150}{2.5}=60$.

Step4: Solve for $y$

Since $y = 150 - x$, substitute $x = 60$ into it. $y=150 - 60 = 90$.

Answer:

60 pounds of wild rice 90 pounds of long grain brown rice