Question

question 6
vihaan bought 7.05 worth of 45 cent stamps and 69 cent stamps. the number of 69 cent stamps was 3 less than the number of 45 cent stamps. solve the equation 0.45s + 0.69(s - 3) = 7.05 for s, to find the number of 45 cent stamps vihaan bought.
vihaan bought 45 cent stamps.
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question 7
emilio is creating a rectangular garden in his back yard. the length of the garden is 14 feet. the perimeter of the garden must be at least 58 feet and no more than 86 feet.
the width of the garden must be at least feet and no more than feet.
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question 8
the length of a rectangle is two inches more than six times the width. the perimeter is 130 inches. find the length and width.
the length is inches, and the width is inches.
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Explanation:

Question 6

Step1: Expand the equation

$0.45s+0.69(s - 3)=0.45s+0.69s-2.07$

Step2: Combine like - terms

$0.45s + 0.69s-2.07=(0.45 + 0.69)s-2.07 = 1.14s-2.07$
So the equation becomes $1.14s-2.07 = 7.05$.

Step3: Isolate the variable term

Add 2.07 to both sides of the equation: $1.14s-2.07 + 2.07=7.05 + 2.07$, which simplifies to $1.14s=9.12$.

Step4: Solve for s

Divide both sides by 1.14: $s=\frac{9.12}{1.14}=8$

Step1: Set up the lower - bound inequality

$P\geq58$, so $2(14 + w)\geq58$.
First, divide both sides by 2: $14 + w\geq29$.
Then subtract 14 from both sides: $w\geq29 - 14=15$.

Step2: Set up the upper - bound inequality

$P\leq86$, so $2(14 + w)\leq86$.
Divide both sides by 2: $14 + w\leq43$.
Subtract 14 from both sides: $w\leq43 - 14 = 29$.

Step1: Substitute into the perimeter formula

$P=2((6w + 2)+w)=2(7w + 2)=14w+4$.
Since $P = 130$, we have the equation $14w+4 = 130$.

Step2: Solve for w

Subtract 4 from both sides: $14w+4 - 4=130 - 4$, so $14w=126$.
Divide both sides by 14: $w=\frac{126}{14}=9$.

Step3: Solve for l

Substitute $w = 9$ into the length formula $l=6w + 2$. Then $l=6\times9+2=54 + 2=56$.

Answer:

8

Question 7

The formula for the perimeter of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Given $l = 14$.