# (Answered) MATH114N Week 5 Assignment: Systems of Linear Equations and Problem Solving

Question

The age of Noelle’s dad is \$_6\$_ less than \$_3\$_ times Noelle’s age. The sum of their ages is \$_74\$_. Find their ages.

# Question

Jason burned 1,400 calories Friday playing 1 hour of basketball and canoeing for 2 hours. On Saturday, he spent 2 hours playing basketball and 3 hours canoeing and burned 2,500 calories. How many calories did he burn per hour when playing basketball?

# Question

Marcus can drive his boat 24 miles down the river in 2 hours but takes 3 hours to return upstream. Find the rate of the boat in still water and the rate of the current.

# Question

Translate to a system of equations:

The sum of two numbers is negative thirty-two. One number is two less than the other.

Call the numbers m and n.

# Question

Bob left home, riding his bike at a rate of 10mph to go to the lake. Cheryl, his wife, left 45 minutes ( 0.75 hour) later, driving her car at a rate of 25mph. How long will it take Cheryl to catch up to Bob?

# Question

Becca is stringing a 28-foot floral garland along the 2 sides and top of a rectangular pergola to prepare for a wedding. The height of the pergola is 4 feet less than the width. Find the height and width of the pergola.

# Question

Translate to a system of equations:

During two years in college, a student earned \$9,500. The second year, she earned \$500 more than twice the amount she earned the first year.

Call the amount that the student earned in the first year f and the amount she earned in the second year s.

Question

Darrin is hanging 200 feet of Christmas garland on the fencing that encloses his rectangular front yard. The length is 5 feet less than 5 times the width. Find the length and width of the fencing. Give the measurements in decimal form.

# Question

Translate to a system of equations:

Daniela invested a total of \$50,000, some in a certificate of deposit (CD) and the remainder in bonds. The amount invested in bonds was \$5,000 more than twice the amount she put into the CD. How much did she invest in each account?

Call the amount that Daniela invested in the CD d and the amount she invested in bonds b.

Note: Do not use the dollar sign or commas when entering numbers.

Question

Translate to a system of equations:

Six times a number plus twice a second number is four. Twice the first number plus four times the second number is eighteen.

Call the first number m and the second number n.

# Question

June needs 45 gallons of punch for a party and has 2 different coolers to carry it in. The bigger cooler is 5 times as large as the smaller cooler. How many gallons can each cooler hold? Enter the answers in decimal form.

# Question

Gail bought 5 pounds of oranges and 2 pounds of bananas for \$14. Her husband later bought 3 pounds of oranges and 6 pounds of bananas for \$18. What was the cost per pound of the oranges and the bananas?

# Question

A small jet can fly 1,435 miles in 5 hours with a tailwind but only 1,215 miles in 5 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

# Question

Felecia left her home to visit her daughter, driving 45mph. Her husband waited for the dog sitter to arrive and left home 20 minutes, or 13 hour later. He drove 55mph to catch up to Felecia. How long before he reaches her?

# Question

Two angles are supplementary. The measure of the larger angle is 4 more than 3 times the measure of the smaller angle. Find the measures of both angles.

# Question

The difference of two complementary angles is 17 degrees. Find the measures of the angles.

# Solution:

Question

The age of Noelle’s dad is \$_6\$_ less than \$_3\$_ times Noelle’s age. The sum of their ages is \$_74\$_. Find their ages.