Solve a System of Equations Using Elimination

Question 1

Diana went to the store to buy socks. She bought 4 sport socks and 4 warm socks for $\$36$. Next time she went to the same store she bought 2 sport socks and 2 warm socks for a total of $\$18$. Using the data she has, find out how much each type of sock costs. Write a system of equations to describe the situation below and solve using elimination.  $Sport \, socks \, cost \, \$4 \, \ \, while \, warm \, socks \, cost \, \$5.$

Accepted Answer

$\$4 \, per \, sport \, socks,\ \, \$5 \, per \, warm \, socks.$

Answer

$\$7 \, per \, sport \, socks,\ \, \$7 \, per \, warm \, socks.$

Answer

$\$5 \, per \, sport \, socks,\ \, \$8 \, per \, warm \, socks.$

Answer

$\$6 \, per \, sport \, socks,\ \, \$3 \, per \, warm \, socks.$

Question 2

Sarah knows she can run 4 kilometers (km) and swim 5 km in 22 minutes. To prove it she swims 3 km and runs 3 km in 15 minutes. Write a system of equations to describe the situation below, solve using elimination.  $Sarah \, can \, run \, a \, km \, in \, 3 \, minutes \, \ \, and \, swim \, a \, km \, in \, 2 \, minutes.$

Accepted Answer

$Swim \, 1 \, km \, in \, 2 \, mins, \, \ \, Run \,  \, 1 \, km \, in \, 3 \, mins.$

Answer

$Swim \, 1 \, km \, in \, 3 \, mins, \, \ \, Run \, 1 \, km \, in \, 4 \, mins.$

Answer

$Swim \, 1 \, km \, in \, 4 \, mins, \, \ \, Run \, 1 \, km \, in \, 2 \, mins.$

Answer

$Swim \, 1 \, km \, in \, 5 \, mins, \, \ \, Run \, 1 \, km \, in \, 6 \, mins.$

Question 3

Isabella teaches both a morning and an evening math class. On the midterm 3 morning students wrote it as well as 2 evening students. A sum of all their marks gave a grand total of 16. For the final there was a grand total of 28 marks, but it was written by 5 morning students and 4 evening students. What is the average mark for both classes? Write a system of equations to describe the situation below, solve using elimination.  $Morning \, class \, has \, an \, average \, of \, 4, \, \ \, but \, the \, evening \, class \, has \, an \, average \, of \, 2.$

Accepted Answer

$Morning \, average: \, 4 \, \ \, Evening \, average: \, 2$

Answer

$Morning \, average: \, 2 \, \ \, Evening \, average: \, 5$

Answer

$Morning \, average: \, 7 \, \ \, Evening \, average: \, 4$

Answer

$Morning \, average: \, 5 \, \ \, Evening \, average: \, 3$

Math Games

Mathematics Florida Standards