Systems of Equations
Word Problems
Word Problems
Two numbers with a difference of two have a sum of 16.
9 and 7
h(t) = |t + 2| + 3; Find h(6)
11
(n2− n − 29) ÷ (n − 6)
n + 5 + 1/n − 6
16n/17 ÷ 8n/6
12/17
There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?
6 chickens and 7 pigs
Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 then how many of each kind did she buy?
2 fancy shirts and 5 plain shirts
w(t) = −2t + 1; Find w(−7)
15
(n2+ 10n + 18) ÷ (n + 5)
n + 5 − 7/n + 5
12/7 ÷ 4/11r
33r/7
(a2− 28) ÷ (a − 5)
a + 5 − 3/a −5
A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current?
boat: 12 mph
current: 9 mph
g(x) = 3x − 3; Find g(−6)
-21
(k2− 7k + 10) ÷ (k − 1)
k − 6 + 4/k − 1
4n/n − 6 ÷ 4n/8n − 48
8
A farmhouse shelters 11 animals. Some are goats and some are ducks. Altogether there are 34 legs. How many of each animal are there?
5 ducks and 6 goats
The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9.
What is the number?
34
h(t) =−2 ⋅ 5-t-1 ; Find h(−2)
-10
(42x2− 33) ÷ (7x + 7)
6x − 6 + 9/7x + 7
7/8r − 40 ÷ 1/8r − 40
7
h(t) = 2 ⋅ 3t + 3; Find h(4 + t)
2 ⋅ 37 + t
Molly's Custom Kitchen Supplies sells handmade forks and spoons. It costs the store $1.70 to buy the supplies to make a fork and $1.30 to buy the supplies to make a spoon. The store sells forks for $5.60 and spoons for $5.40. Last April Molly's Custom Kitchen Supplies spent $37.90 on materials for forks and spoons. They sold the finished products for a total of $147.20. How many forks and how many spoons did they make last April?
7 forks and 20 spoons
p(a) = −43a; Find p(−1)
-1/64
(2x2− 17x − 38) ÷ (2x + 3)
x − 10 − 8/2x + 3
a − 4/a2− 2a − 8 ÷ 1/a − 5
a − 5/a + 2
16x − 56/8 ÷ 8x − 28/4
1