Writing systems of Equations from word problems
Write an equation for the following situation:
Becky is buying almonds and raisins to make trail mix. Almonds cost $2 per pound and raisins cost $1.50 per pound. She spends 30 dollars in total.
Use x for almonds and y for raisins.
2x+1.50y=30
Solve the system of equations.
3x + 2y = 12
x + y = 4
(4,0)
Solve the system of equations.
2x-5y=58
-2x+10y=92
y= 30
x=104
For entrepreneur day at school, Lin made paper airplanes and stickers to sell. She sells the paper airplanes for $4 each and the stickers for $1.50 each. Lin hopes to make at least $50 in sales. Write an inequality to match the situation.
4a + 1.50s >= 50
Is the coordinate pair (1,2) a solution to the equation 4y +7x = 15?
yes
A farmer has 40 animals consisting of chickens and cows. If there are twice as many chickens as cows, write a system of equations to represent the number of each type of animal.
x+y=40
2y=x
x = chickens
y = cows
Given the equations y=x−4 and x+y=10, solve using substitution.
(7,3)
Solve using elimination
4x+3y=18
−4x+5y=2
(21/8 , 5/2)
The drama club is selling tickets for their upcoming performance. Student tickets (s) are $7 each and adult tickets (a) are $12.50 each. The theater seats 250 people. The department wants to raise at least $2500. Write a system of inequalities to represent the situation.
7s + 12.50a >= 2500
s+a<=250
Convert this equation into slope intercept form.
2x - 5y = -10
2 + 2/5x = y
An art supply store sells paintbrushes for $3 each and canvases for $15 each. If a customer buys 8 items and spends a total of $54, write a system of equations to represent this scenario.
3p +15c=54
p+c=8
Use substitution to solve the system: y=3x+1 and 4x−y=5
(6,19)
Solve using elimination
3x+2y=14
5x−3y=7
(56/19, 49/19)
A club sells movie tickets (m) and concert tickets (c) to raise money. Movie tickets cost $8, concerts $12. They want to earn at least $480, but can sell no more than 40 total tickets. Write a system of inequalities to represent the situation.
8m+12c >= 480
m+c <= 40
Explain how you can tell if a system of equations has no solutions from the equations and from a graph.
Graph has parallel lines.
Equations have same slope but different y intercepts.
A dining hall had a total of 25 tables—some long rectangular tables and some round ones. Long tables can seat 8 people. Round tables can seat 6 people. On a busy evening, all 190 seats at the tables are occupied.
s + l = 25
8 L + 6 s = 190
Use substitution to solve the system: y=3x+1 and 4x−2y=5
(-7/2 , -19/2)
Solve using elimination
6x+4y=20
9x−8y=12
(52/21, 9/7)
A student sells bracelets (b) and necklaces (n). Each bracelet takes 2 hours, each necklace takes 3 hours, and she has no more than 18 hours to work. She must make at least 10 items. Write a system of inequalities to represent the situation.
2b+3n<=18
b+n>=10
Describe what the graph of the inequality y>3x+2.
Include y intercepts, slope, solid or dashed line, and region that should be shaded (below or above line).
slope = 3
y int = 2
dashed line
region above line should be shaded
At a poster shop, Han paid $16.80 for 2 large posters and 3 small posters of his favorite band. Kiran paid $14.15 for 1 large poster and 4 small posters of his favorite TV shows. Posters of the same size have the same price.
16.80 = 2L+ 3s
14.15 = L + 4s
-x-2y=20
x+y=10
(40, -30)
8x+12y=480
x+y=40
(0,40)
Han is buying decorations for a school dance. He wants to purchase more than 15 table linens in the colors black and gold. The black table linens cost $10 per linen, and the gold table linens cost $14 per linen. Han has a budget of $200 for the table linens he plans to purchase for the event.
b + g > 15
10b+14g <= 200
Describe what the graph of the inequality 2x - 5y >= -10.
Include y intercepts, slope, solid or dashed line, and region that should be shaded (below or above line).
line y = 2 + 2/5x
y int is 2
slope is 2/5
solid line
shaded below