MATH

Math 8.1

64. Baking Kelsey needs 2 3 cup of sugar for the cookie recipe she wants to make. She only has 1 4 cup of sugar and will borrow the rest from her neighbor. Let s equal the amount of sugar she will borrow. Solve the equation 1 4 + s = 2 3 to find the amount of sugar she should ask to borrow.

65. Construction Miguel wants to drill a hole for a 5 8 -inch screw. The screw should be 1 12 inch larger than the hole. Let d equal the size of the hole he should drill. Solve the equation d + 1 12 = 5 8 to see what size the hole should be. Writing Exercises

66. Is −18 a solution to the equation 3x = 16 − 5x ? How do you know?

67. Write a word sentence that translates the equation y − 18 = 41 and then make up an application that uses this equation in its solution.

Math 8.2

104. Balloons Ramona bought 18 balloons for a party. She wants to make 3 equal bunches. Find the number of balloons in each bunch, b, by solving the equation 3b = 18.

105. Teaching Connie’s kindergarten class has 24 children. She wants them to get into 4 equal groups. Find the number of children in each group, g, by solving the equation 4g = 24. 8.2 EXERCISES Chapter 8 Solving Linear Equations 685

106. Ticket price Daria paid $36.25 for 5 children’s tickets at the ice skating rink. Find the price of each ticket, p, by solving the equation 5p = 36.25.

107. Unit price Nishant paid $12.96 for a pack of 12 juice bottles. Find the price of each bottle, b, by solving the equation 12b = 12.96.

108. Fuel economy Tania’s SUV gets half as many miles per gallon (mpg) as her husband’s hybrid car. The SUV gets 18 mpg. Find the miles per gallons, m, of the hybrid car, by solving the equation 1 2 m = 18.

109. Fabric The drill team used 14 yards of fabric to make flags for one-third of the members. Find how much fabric, f, they would need to make flags for the whole team by solving the equation 1 3 f = 14.

110. Frida started to solve the equation −3x = 36 by adding 3 to both sides. Explain why Frida’s method will result in the correct solution.

111. Emiliano thinks x = 40 is the solution to the equation 1 2 x = 80. Explain why he is wrong.

Math 2.2

In the following exercises, use algebraic expressions to solve the problem.

143. Car insurance Justin’s car insurance has a $750 deductible per incident. This means that he pays $750 and his insurance company will pay all costs beyond $750. If Justin files a claim for $2,100, how much will he pay, and how much will his insurance company pay?

144. Home insurance Pam and Armando’s home insurance has a $2,500 deductible per incident. This means that they pay $2,500 and their insurance company will pay all costs beyond $2,500. If Pam and Armando file a claim for $19,400, how much will they pay, and how much will their insurance company pay?

145. Explain why “the sum of x and y” is the same as “the sum of y and x,” but “the difference of x and y” is not the same as “the difference of y and x.” Try substituting two random numbers for x and y to help you explain.

146. Explain the difference between “4 times the sum of x and y” and “the sum of 4 times x and y.”