Writing and Solving Equations in Two Variables

Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet. She writes and solves the equation to find the width of the run. Which statements are true of the solution? Check all that apply. The value of w is 10 feet. The value of w can be zero. The value of w cannot be a negative number. Substitution is used to replace the variable l with a value of 20. The subtraction property of equality is used to isolate the term with the variable w.

- The value of w cannot be a negative number. - Substitution is used to replace the variable l with a value of 20. - The subtraction property of equality is used to isolate the term with the variable w.

An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equation to solve is 2a + b = 15.7. If we recall that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, which lengths make sense for possible values of b? Select two options. -2 in. 0 in. 0.5 in. 2 in. 7.9 in.

0.5 2

Wei has $150.00 to make a garland using 60-cent balloons. He wants to purchase 100 blue balloons and some number of white balloons. He learns that the white balloons are on sale for half price. He writes and solves an equation to find the number of white balloons he can purchase. Which models can be used to solve the problem?

0.60b + 0.30w = 150; 60+0.30 w=150

What is the value of a in the equation 5a-10b= 45 , when b=3 ? 3 15 21 39

3

Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. If Hugh bought 3 magazines, how many books did he buy? The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books.

4 books

Fiona bought some socks that cost $4.95 for each pair and some belts that cost $6.55 each. Fiona spent $27.95 in all. Let a represent the number of pairs of socks purchased and b the number of belts purchased.

4.95a + 6.55b = 27.95

What is the value of x in the equation 8x - 2y = 48, when y = 4? 6 7 14 48

7

What is the value of x in the equation 4x+8y=40 , when y=0.8 ? 4.6 8.4 10 12

8.4

Sophie is buying fabric to make items for a craft fair. The table shows some combinations of how much of each color fabric she might buy. Which equations model the total yards of fabric Sophie will buy? Check all that apply.

A,D,E

The perimeter of a scalene triangle is 14.5 cm. The longest side is twice that of the shortest side. Which equation can be used to find the side lengths if the longest side measures 6.2 cm?

B. 9.3+b=14.5

Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. Let m represent the number of magazines and b represent the number of books. Which equation models the situation?

C

Last month Maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. Let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. If she hiked a total of 90 miles, which equation can be used to find the number of times Maria hiked each trail? x + y = 90 5x - 10y = 90 90 - 10y = 5x 90 + 10y = 5x

C.90 - 10y = 5x

The isosceles triangle has a perimeter of 7.5 m. Which equation can be used to find the value of x if the shortest side, y, measures 2.1 m?

D. 2.1x+2x=7.5

Hanna shops for socks that cost $2.99 for each pair and blouses that cost $12.99 each. Let x represent the number of pairs of socks purchased, and let y represent the number of blouses purchased. Which equation models the purchases she made with $43.92? x + y = 15.98 x + y = 43.92 43.92x - 2.99y = 12.99 2.99x + 12.99y = 43.92

D.2.99x + 12.99y = 43.92

What error did Malik make first when solving the equation ? Malik did not multiply correctly. Malik added 240 to each side of the equation. Malik did not multiply correctly. Malik substituted 60 for y instead of x.

Malik substituted 60 for y instead of x.

Maya spent her allowance on playing an arcade game a few times and riding the Ferris wheel more than once. Write about what additional information you would need to create a two-variable equation for the scenario. What kind of problem could you solve with your equation?

Sample Response: To write a two-variable equation, I would first need to know how much Maya's allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game.

What is the value of x in the equation 3x-4y=65 , when y=4

x=27

Hans is planting a garden with snapdragons and daisies. The table shows some possible combinations of the two plants. If Hans plants 29 daisies, how many snapdragons will he plant? The equation_______________models the scenario. He will plant ________ snapdragons

x=45-y 16

Jillian's school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation , where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how may adult tickets were sold?

168 adult tickets

What is the value of a in the equation 3a+b= 54 , when b=9 ? 15 18 21 27

15