Question

directions: for 1 - 2, determine the equation that is represented by each situation. 1. ms. blalock went to the store and bought three dvds for $15 each and a tv for 25% off. if she spent a total of $345, which equation could be used to find the original price of the tv, x? (1) 0.75x + 45 = 345 (2) 0.25x + 45 = 345 (3) 0.75x + 15 = 345 (4) 0.25x + 15 = 345 2. the length of a rectangle is 8 more than half the width. if the perimeter of the rectangle is 94 feet, which of the following equations could be used to calculate the width of the rectangle? (1) (2(x/2 + 8))+x = 94 (2) 2(x/2 + 8)=94 (3) 2(x/2 + 8)+2x = 94 (4) (x/2 + 8)(x)=94

Explanation:

Step1: Analyze the TV - purchase problem

Let the original price of the TV be $x$. She got a 25% off, so she paid $(1 - 0.25)x=0.75x$. She also bought 3 DVDs at $15$ each, so the total amount she spent is $0.75x + 3\times15$. And we know she spent $345$ in total. So the equation is $0.75x+45 = 345$.

Step2: Analyze the rectangle - perimeter problem

Let the width of the rectangle be $x$. The length of the rectangle is 8 more than half of the width, so the length is $\frac{x}{2}+8$. The perimeter of a rectangle is given by $P = 2(l + w)$, where $l$ is the length and $w$ is the width. So $P=2((\frac{x}{2}+8)+x)$. And we know $P = 94$. So the equation is $2((\frac{x}{2}+8)+x)=94$.

Answer:

1. The correct equation for the TV - purchase problem is $0.75x + 45=345$.
2. The correct equation for the rectangle - perimeter problem is $2((\frac{x}{2}+8)+x)=94$.