Solving For One Variable
Is it a solution?
Equivalent Equations
What does it mean?
Writing Equations
100
For a dance competition, each girl needs 0.5 feet of ribbon for their hair bows. The relationship between the total about of ribbon needed, r, and the number of girls, g, can be modeled with the following equation:
0.5g = r.
Rewrite the equation by solving for g.
g = r/0.5
100
Is 2 a solution to the following equation:
5x = 10?
Explain or show how you know.
Yes
5(2) = 10
100
Is 2y + 2x = 12 equivalent to y + x = 12? Explain/ show how you know
No, since they are both already equal to 12 on the right sides, but the left sides of the equations do not match.
100
The graph below shows the relationship between the amount of money in a student's savings account and the number of weeks since the student started depositing money.
What does the point (20, 3000) mean in this context?
The student has $3,000 dollars in their bank account after 20 weeks.
100
A pound of grapes costs $3. Write an equation that represents the relationship between p pounds of grapes and T, the total cost.
3p = T
200
The area of a parallelogram can be modeled by the following equation: B x H = A. Rewrite the equation solving for B.
B = A/H or
B = A ÷ H
200
The following graph represents the relationship between water in a tank and time. How much water is left in the tank after 10 minutes?
250 gallons
200
Are the equations 4x - 0.5 = 7 and 8x = 15 equivalent? Show or explain your reasoning
Yes, 4x - 0.5 = 7 turns into 4x = 7.5 if we add 0.5 to both sides. Then we can multiply the whole equation by 2 to get 8x = 15
200
The number of calories in a gram of protein is 4 and the number of calories in a gram of fat is 9. The relationship between fat and protein can be modeled by this equation: 4p + 9f = 100. What would a solution to the equation 4p + 9(4) = 100 mean in this situation?
The amount of protein needed to get to 110 calories when we have 4 grams of fat
200
The cost of making t-shirts at Shirt Company is $7 per shirt plus a $9 shipping charge. Write an equation that represents the relationship between s, the number of shirts, and c, the total cost of making the t-shirts.
7s + 9 = c
300
In a particular class, the number of girls is 3 times the number of boys. Write an equation that models the relationship between b boys and g girls. Then, rewrite the equation solving for the other variable.
g = 3b
b = g/3
300
Solve the equation:
0.5x + 7 = 22
x = 30
300
Is 7 + 3b + 2 = 12 equivalent to 3b = 6? Explain or show your reasoning.
No, the first equation solved would give b = 1 and the second equation solved would give b = 2
300
This is the graph of 6a + 9f = 75 which represents the amounts of almonds and figs that cost $75. 
What does it mean if a point is below the line?
The amount of almonds and figs costs less than $75 dollars.
300
A group of students is raising money for the wrestling team. The students plan to raise a total of $1500 for their team with each person raising an equal amount. Write an equation that shows the relationship between n, the number of students, and a, the amount each students needs to raise.
1500/n = a
or 1500 ÷ n = a
400
The equation L = 400 - 1.5m represents the relationship between liters in a tank of water and minutes. Rewrite the equation by solving for m.
m = (400 - L)/1.5
m = (L - 400)/-1.5
400
The following equation represents the relationship between calories from protein and fat in a snack:
4p + 9f = 95
Is p = 3.5 and f = 9 a solution? Show or explain how you know.
Yes
4(3.5) + 9(9) = 95
400
Is 3x - 5y = 10 equivalent to
y =(10 - 3x)/-5
Show or explain your reasoning
Yes, if we solve for y in the first equation, we get the second equation.
400
The number of calories in a gram of protein is 4 and the number of calories in a gram of fat is 9. What would a solution to the equation 4p + 9f = 100 mean in this situation?
How many grams of fat and grams of protein we need to get to 100 calories
400
A tank with 150 liters in it drains at a rate of 3.5 liters a minute. Write an equation to represent the relationship between L, the water left in the tank, and m, the number of minutes.
150 - 3.5m = L
500
The equation L = 500 + 1.2m represents the relationship between liters in a tank, L, and minutes, m. Solve the equation for m. Then, plug into one of the equations to find the number of minutes it takes for the tank to fill to 644 liters.
m = (L-500)/1.2
m = 120
500
Is x = ⅓ and y = 2.5 a solution to the following equation? 9x -0.5 + 7y -3 = 17.5
Explain/show how you know
No, 9(⅓) - 0.5 + 7(2.5) -3 = 17 not 17.5
500
Are the following equations equivalent? Explain/show your reasoning
y = (3x + 9)/5
x = (5y - 9)/3
Yes, if we solve the first equation for x is will give us
x = (5y-9)/3
500
Jimmy is hosting a birthday party at the ice rink. The cost per person is $15 and will include a rental fee of $50. To get everybody there, transportation will cost $30. The total cost of Jimmy's birthday party is $435. The following equation represents the situation: 50 + 15n + 30 = 305
What does a solution to this equation mean?
The number of people attending the party when it costs $305 dollars
500
Bill's age is two years older than 3 times the difference between his little sister's age and his little brother's age. If Bill's age can be represented with B, his little sister's age can be represented with A, and his little brother's age can be represented with C, write an equation to represent the relationship between Bill's age and his siblings' ages.
B = 3(A-B)+2