Exercises

1. 1. If \(y=x+11\) and \(x=3\), find the value of \(y\).
   2. If \(y=\dfrac{x}{4}\) and \(y=7\), find the value of \(x\).
   3. If \(y=x-7\) and \(x=4\), find the value of \(y\).
2. 1. If \(y=3x-2\) and \(x=6\), find the value of \(y\).
   2. If \(y=\dfrac{x}{3}-1\) and \(x=27\), find the value of \(y\).
   3. If \(y=\dfrac{x}{7}+4\) and \(y=9\), find the value of \(x\).
3. The equation \(B=\dfrac{p}{8}-3\) represents the number of batches of cookies, \(B\), that are needed to have a bake sale where \(p\) people are expected to attend.
   1. If \(128\) people are expected to attend, how many batches of cookies are needed?
   2. If \(7\) batches of cookies are prepared, how many people are the bake sale organizers prepared to have attend?
4. The equation \(C=2d+7\) represents the cost, \(C\), for Kris to pay \($7\) for a large popcorn and \(d\) dollars each for \(2\) drinks at the movie theatre.
   1. If Kris' total cost was \($16\), how much did Kris pay for each drink?
   2. If each drink costs \($5.25\), how much would the total cost be?
5. Consider the following sequence of images.
   
   1. Write an equation to represent the relationship between the term number, \(n\), and the number of shaded squares, \(S\), in image \(n\).
   2. How many squares are used to form the \(10^{th}\) image?
   3. Which term number corresponds to the image with \(125\) squares?
6. The following math machine first adds \(3\) to the input, and then multiplies the result by \(5\). If \(m\) is the input, then the output of the machine will be \(5(m+3)\).
   

   Source: Machine - whanwhanai/iStock/Getty Images

   1. Determine the output of the machine for inputs \(m=1\) and \(m = 6\).
   2. If the output of the machine is \(35\), then what was the input?
   3. If the output of the machine is \(225\), then what was the input?
7. In \(\Delta ABC\), we are given that \(\angle A = 50^{\circ}\)and \(\angle B = (3x+5)^{\circ}\) where \(x\) is an unknown integer.
   
   1. If \(x = 10\), then what must be the measure of \(\angle C\)?
   2. If \(\angle C = 101^{\circ}\), then what must be the value of \(x\)?
   3. What is the largest possible value of \(x\)?
8. A math machine performs the following sequence of operations on input \(n\): Calculate the square root of \(n\), then multiply this number by \(2\), and then add \(14\) to the result.
   1. Determine the output of the machine when the inputs are \(n = 4\) and \(n = 25\). 
   2. Given an unknown input \(n\), determine an expression for the output of the machine.
   3. If the machine has an output of \(16\), what was the input \(n\)?
   4. If the machine has an output of \(40\), what was the input \(n\)?
   5. If the machine has an output of \(p\), what was the input?
      Your answer will need to be a mathematical expression involving the variable \(p\).