Susan and Jan sold T-shirts for a fundraiser. Together they sold 85.
Jan sold 5 less than twice the amount of Susan. Write an equation to
model the situation so that we can find how many shirts each girl sold.
Linda was selling tickets for the school play. She sold 10 more adult
tickets than children tickets and she sold twice as many senior tickets as
children tickets. Adult tickets cost $5, senior tickets cost $3 and children
tickets cost $2. Linda made $700. Write an equation to model the situation
so that we can find the amount of tickets sold to adults, children, and seniors.
Could someone show me how to do these problems
Certainly! Let's start by breaking down the given information and writing equations based on the problems.
Problem 1:
Let's assume that Susan sold x t-shirts.
According to the problem, Jan sold 5 less than twice the amount of Susan's t-shirts. So Jan sold (2x - 5) t-shirts.
The total number of t-shirts sold is 85. Therefore, we can write the equation:
x + (2x - 5) = 85
Simplifying the equation, we have:
3x - 5 = 85
Now we can solve for x:
3x = 85 + 5
3x = 90
Divide both sides by 3:
x = 90 / 3
x = 30
So, Susan sold 30 t-shirts and Jan sold (2x - 5) = 2(30) - 5 = 55 t-shirts.
Problem 2:
Let's assume the number of children tickets sold is x.
According to the problem, Linda sold 10 more adult tickets than children tickets, which means the number of adult tickets sold is (x + 10).
Linda sold twice as many senior tickets as children tickets, so the number of senior tickets is 2x.
The total income from ticket sales is $700. Therefore, we can write the equation:
2(5)(x + 10) + 3(2x) + 2x = 700
Simplifying the equation, we have:
10(x + 10) + 6x + 2x = 700
10x + 100 + 8x = 700
18x + 100 = 700
Now we can solve for x:
18x = 700 - 100
18x = 600
Divide both sides by 18:
x = 600 / 18
x ≈ 33.33
Since we cannot have a fraction of a ticket, we round down to the nearest whole number. So, the number of children tickets sold is 33.
The number of adult tickets sold is (x + 10) = 33 + 10 = 43.
The number of senior tickets sold is 2x = 2(33) = 66.
Therefore, Linda sold 43 adult tickets, 33 children tickets, and 66 senior tickets.
That's how you can solve these problems by setting up equations and solving them. I hope this helps! Let me know if you have any further questions.