solve each word problem using a system of equations. use substitution or elimination.\n1. one number added…

solve each word problem using a system of equations. use substitution or elimination.\n1. one number added to three times another number is 24. five times the first number added to three times the other number is 36. find the numbers.\n2. ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large cups for $2.50. if ashley sold a total of 155 cups of lemonade for $265, how many cups of each type did she sell?\n3. your family goes to a southern - style restaurant for dinner. there are 6 people in your family. some order the chicken dinner for $14 and some order the steak dinner for $17. if the total bill was $99, how many people ordered each dinner?\n4. tickets to a movie cost $7.25 for adults and $5.50 for students. a group of friends purchased 8 tickets for $52.75. how many adult tickets and student tickets were purchased?\n5. a sporting goods store sells right - handed and left - handed baseball gloves. in one month, 12 gloves were sold for a total of $561. right - handed gloves cost $45 each and left - handed gloves cost $52 each. how many of each type of glove were sold?

solve each word problem using a system of equations. use substitution or elimination.\n1. one number added to three times another number is 24. five times the first number added to three times the other number is 36. find the numbers.\n2. ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large cups for $2.50. if ashley sold a total of 155 cups of lemonade for $265, how many cups of each type did she sell?\n3. your family goes to a southern - style restaurant for dinner. there are 6 people in your family. some order the chicken dinner for $14 and some order the steak dinner for $17. if the total bill was $99, how many people ordered each dinner?\n4. tickets to a movie cost $7.25 for adults and $5.50 for students. a group of friends purchased 8 tickets for $52.75. how many adult tickets and student tickets were purchased?\n5. a sporting goods store sells right - handed and left - handed baseball gloves. in one month, 12 gloves were sold for a total of $561. right - handed gloves cost $45 each and left - handed gloves cost $52 each. how many of each type of glove were sold?

Answer

1.

Step1: Set up equations

Let the first number be (x) and the second number be (y). The equations are (x + 3y=24) (Equation 1) and (5x+3y = 36) (Equation 2).

Step2: Subtract Equation 1 from Equation 2

((5x + 3y)-(x + 3y)=36 - 24) (5x+3y-x - 3y=12) (4x=12), so (x = 3).

Step3: Substitute (x = 3) into Equation 1

(3+3y=24) (3y=24 - 3=21), so (y = 7).

Answer:

The two numbers are (3) and (7).

2.

Step1: Set up equations

Let the number of small cups be (x) and the number of large cups be (y). We have (x + y=155) (Equation 1) and (1.25x+2.5y=265) (Equation 2). From Equation 1, (x=155 - y).

Step2: Substitute (x = 155 - y) into Equation 2

(1.25(155 - y)+2.5y=265) (193.75-1.25y + 2.5y=265) (1.25y=265 - 193.75 = 71.25) (y = 57).

Step3: Find (x)

Substitute (y = 57) into (x=155 - y), (x=155-57 = 98).

Answer:

Ashley sold (98) small cups and (57) large cups.

3.

Step1: Set up equations

Let the number of people who ordered chicken dinner be (x) and the number of people who ordered steak dinner be (y). We have (x + y=6) (Equation 1) and (14x+17y=99) (Equation 2). From Equation 1, (x=6 - y).

Step2: Substitute (x = 6 - y) into Equation 2

(14(6 - y)+17y=99) (84-14y+17y=99) (3y=99 - 84=15) (y = 5).

Step3: Find (x)

Substitute (y = 5) into (x=6 - y), (x=6 - 5=1).

Answer:

(1) person ordered chicken dinner and (5) people ordered steak dinner.

4.

Step1: Set up equations

Let the number of adult tickets be (x) and the number of student tickets be (y). We have (x + y=8) (Equation 1) and (7.25x+5.5y=52.75) (Equation 2). From Equation 1, (x=8 - y).

Step2: Substitute (x = 8 - y) into Equation 2

(7.25(8 - y)+5.5y=52.75) (58-7.25y+5.5y=52.75) (- 1.75y=52.75 - 58=-5.25) (y = 3).

Step3: Find (x)

Substitute (y = 3) into (x=8 - y), (x=8 - 3=5).

Answer:

(5) adult tickets and (3) student tickets were purchased.

5.

Step1: Set up equations

Let the number of right - handed gloves be (x) and the number of left - handed gloves be (y). We have (x + y=12) (Equation 1) and (45x+52y=561) (Equation 2). From Equation 1, (x=12 - y).

Step2: Substitute (x = 12 - y) into Equation 2

(45(12 - y)+52y=561) (540-45y+52y=561) (7y=561 - 540 = 21) (y = 3).

Step3: Find (x)

Substitute (y = 3) into (x=12 - y), (x=12 - 3=9).

Answer:

(9) right - handed gloves and (3) left - handed gloves were sold.