ALG U5 L8: Modeling with Systems of Equations Part 3
Setup and solve a system of equations for each problem below.
1.) Jane is 4 times as old as Karen. Jane’s age decreased by Karen’s age is 21. Find the age of each.
j = 4k
j – k = 21
4k – k = 21
3k = 21
k=7
j = 4k
j = 4(7)
j = 28
Karen is 7 years old.
Jane is 28 years old.
2.) The sum of the ages of two sisters is 32 years. The difference in their ages is 4 years. Find the age of each.
a + b = 32
a–b=4
2a = 36
a = 18
18 + b = 32
b = 14
The sisters’ ages are 14 and 18.
3.) There were 100 more balcony tickets than main-floor tickets sold for a concert. The balcony tickets sold for
$4 and the main-floor tickets sold for $12. The total amount of sales for both types of tickets was $3056. Find
the number of balcony and main-floor tickets sold.
b = m + 100
4b + 12m = 3056
4(m + 100) + 12m = 3056
4m + 400 + 12m = 3056
16m + 400 = 3056
16m = 2656
m = 166
b = 166 + 100
b = 266
166 main-floor tickets were sold and 266 balcony tickets were sold.
4.) A local theater is showing an animated movie. They charge $5 per ticket for a child and $12 per ticket for an
adult. They sell a total of 342 tickets and make a total of $2256. Determine how many adult and how many
child tickets were sold.
5c + 12a = 2256
c + a = 342
5c + 12a = 2256
-5c – 5a = -1710
7a = 546
a = 78
c + 78 = 342
c = 264
78 adults tickets
264 child tickets