SAT Math Practice: Setting Up a System of Equations

1. John and Jason are selling plants at the annual plant sale. John sells 12 tomato plants and 14 cucumber plants for $306. Jason sells 4 tomato plants and 16 cucumber plants for $218. Which system of equations can be used to solve for the price of each tomato plant, $t$ , and each cucumber plant, $c$ ?

$12c+15t=306$ $4c+16t=218$

$12t+4c=306$ $15t+16c=218$

$12c+4t=218$ $15c+16t=306$

$12t+15c=306$ $4t+16c=218$

2. The price of a bottle of Coke is $2.75. The price of a bottle of Pepsi is $2.80. If Nick buys 18 bottles of soda for his party which cost him a total of $50, which of the following system of equations can be used to solve for the number of bottles of Coke, $c$ , and Pepsi, $p$ , that Nick bought?

$c+p=50$ $2.75c+2.80p=18$

$c+p=18$ $2.75c+2.80p=50$

$c+p=50$ $2.75p+2.80c=18$

$c+p=18$ $2.75p+2.80c=50$

3. Ms. Brown and Ms. Fisher want to take their third grade students on a trip to the aquarium. Ms. Brown’s class spends $568 on 25 children tickets and 6 adult tickets, and Ms. Fisher’s class spends $532 on 26 children tickets and 4 adult tickets. Which system of equations can be used to solve for the price of each child ticket, $c$ , and each adult ticket, $a$ ?

$25a+6c=568$ $26a+4c=532$

$25c+6a=568$ $26c+4a=532$

$25c+6a=532$ $26c+4a=568$

$25a+6c=532$ $26a+4c=568$

4. Lily wants to cater food for a large fundraiser. She decides that 50 trays of food should be enough to feed everyone. Each tray of pasta costs $27 and each tray of salad costs $32. If $1,137 is spent on food, which of the following system of equations can be used to solve for the number of trays of pasta, $p$ , and salad, $s$ , that Lily catered?

$27p+32s=1137$ $p+s=50$

$27p+32s=50$ $p+s=1137$

$27s+32p=50$ $p+s=1137$

$27s+32p=1137$ $p+s=50$

5. A printing company needs to purchase more ink. Each black ink cartridge costs $38 and each colored ink cartridge costs $44. The company spends $652 on 42 total cartridges to replenish its ink supply. If $b$ represents the number of black ink cartridges purchased and $c$ represents the number of colored ink cartridges purchased, which of the following system of equations could be used to solve for both $b$ and $c$ ?

$38b+44c=652$ $b+c=42$

$38b+44c=42$ $b+c=652$

$38c+44b=652$ $b+c=42$

$38c+44b=42$ $b+c=652$