1 priya is buying raisins and almonds to make trail mix. almonds cost $5.20 per pound and raisins cost $2.75…
1 priya is buying raisins and almonds to make trail mix. almonds cost $5.20 per pound and raisins cost $2.75 per pound. priya spent $11.70 buying almonds and raisins. the relationship between pounds of almonds a, pounds of raisins r, and the total cost is represented by the equation 5.20a + 2.75r = 11.70. how many pounds of raisins did priya buy if she bought the following amounts of almonds: a. 2 pounds of almonds b. 1.06 pounds of almonds c. 0.64 pounds of almonds d. a pounds of almonds 2 here is a linear equation in two variables: 2x + 4y - 31 = 123. solve the equation for x. then solve the equation for y.
Answer
1.
a.
Explanation:
Step1: Substitute $a = 2$ into equation
Substitute $a = 2$ into $5.20a+2.75r = 11.70$. We get $5.20\times2+2.75r=11.70$.
Step2: Calculate the product
$5.20\times2 = 10.40$, so the equation becomes $10.40 + 2.75r=11.70$.
Step3: Isolate the term with $r$
Subtract $10.40$ from both sides: $2.75r=11.70 - 10.40=1.30$.
Step4: Solve for $r$
Divide both sides by $2.75$: $r=\frac{1.30}{2.75}=\frac{130}{275}=\frac{26}{55}\approx0.47$ pounds.
Answer:
$\frac{26}{55}\approx0.47$ pounds
b.
Explanation:
Step1: Substitute $a = 1.06$ into equation
Substitute $a = 1.06$ into $5.20a + 2.75r=11.70$. We have $5.20\times1.06+2.75r=11.70$.
Step2: Calculate the product
$5.20\times1.06 = 5.512$, so the equation is $5.512+2.75r=11.70$.
Step3: Isolate the term with $r$
Subtract $5.512$ from both sides: $2.75r=11.70 - 5.512 = 6.188$.
Step4: Solve for $r$
Divide both sides by $2.75$: $r=\frac{6.188}{2.75}=\frac{6188}{2750}=\frac{1547}{687.5}\approx2.25$ pounds.
Answer:
$\frac{1547}{687.5}\approx2.25$ pounds
c.
Explanation:
Step1: Substitute $a = 0.64$ into equation
Substitute $a = 0.64$ into $5.20a+2.75r = 11.70$. We obtain $5.20\times0.64+2.75r=11.70$.
Step2: Calculate the product
$5.20\times0.64 = 3.328$, so the equation is $3.328+2.75r=11.70$.
Step3: Isolate the term with $r$
Subtract $3.328$ from both sides: $2.75r=11.70 - 3.328 = 8.372$.
Step4: Solve for $r$
Divide both sides by $2.75$: $r=\frac{8.372}{2.75}=\frac{8372}{2750}=\frac{2093}{687.5}\approx3.05$ pounds.
Answer:
$\frac{2093}{687.5}\approx3.05$ pounds
d.
Explanation:
Step1: Isolate the term with $r$
Start with $5.20a+2.75r = 11.70$. Subtract $5.20a$ from both sides: $2.75r=11.70 - 5.20a$.
Step2: Solve for $r$
Divide both sides by $2.75$: $r=\frac{11.70 - 5.20a}{2.75}=\frac{1170 - 520a}{275}=\frac{234 - 104a}{55}$ pounds.
Answer:
$\frac{234 - 104a}{55}$ pounds
2.
Solve for $x$:
Explanation:
Step1: Isolate the term with $x$
Start with $2x + 4y-31 = 123$. Add $31$ to both sides: $2x+4y=123 + 31=154$.
Step2: Isolate $x$
Subtract $4y$ from both sides: $2x=154 - 4y$. Then divide both sides by $2$: $x=\frac{154 - 4y}{2}=77 - 2y$.
Answer:
$x = 77 - 2y$
Solve for $y$:
Explanation:
Step1: Isolate the term with $y$
We know $2x+4y = 154$ from the previous step. Subtract $2x$ from both sides: $4y=154 - 2x$.
Step2: Solve for $y$
Divide both sides by $4$: $y=\frac{154 - 2x}{4}=\frac{77 - x}{2}= \frac{77}{2}-\frac{x}{2}$.
Answer:
$y=\frac{77}{2}-\frac{x}{2}$