1. Let the width be $w$ and the length be $l$. Given $l = 2w$ and perimeter $P = 2(l + w) = 88$. Substituting, $2(2w + w) = 88 \Rightarrow 6w = 88 \Rightarrow w = \frac{44}{3}$. Then $l = \frac{88}{3}$. Dimensions are width $\frac{44}{3}$ cm and length $\frac{88}{3}$ cm.
2. Let $x$ kg be the 40% flour and $y$ kg be the 70% flour. Then $x + y = 45$ and $0.4x + 0.7y = 0.6 \cdot 45 = 27$. Solving: from first equation, $x = 45 - y$. Substitute: $0.4(45 - y) + 0.7y = 27 \Rightarrow 18 - 0.4y + 0.7y = 27 \Rightarrow 0.3y = 9 \Rightarrow y = 30$. Then $x = 15$. So 15 kg of 40% flour and 30 kg of 70% flour were used.
3. Let $p$ be plane speed in still air and $w$ be wind speed. Then $p + w = 158$ and $p - w = 112$. Adding equations: $2p = 270 \Rightarrow p = 135$. Subtracting: $2w = 46 \Rightarrow w = 23$. Plane speed is 135 km/hr, wind speed is 23 km/hr.
4. Let $c$ be number of cars and $v$ be number of vans. Then $c + v = 30$ and $100c + 200v = 4000$. Simplify second equation: $c + 2v = 40$. Subtract first equation: $(c + 2v) - (c + v) = 40 - 30 \Rightarrow v = 10$. Then $c = 20$. Sam rented 20 cars and 10 vans.
Parent Tip: Review the logic above to help your child master the concept of solving systems of equations word problems worksheets.
