Question

Solve for x.
7 - (2x + 11) + 3(3 - x) = 20
-3
-4


One number is five more than three times another. If their difference is 35, what is the larger number?
15
50
65


Cool Scoops ice cream shop offers 42 different one-topping sundaes. If there are 7 flavors of ice cream, how many toppings are there?
6
5
3

Answer 1

#1:

7 - (2x+11) + 3(3-x) = 20
7 - 2x - 11 + 9 - 3x = 20
5 - 5x = 20
-5x = 15
x = -3


#2:
x = one number
y = the other number
x = 5 + 3y
x-y = 35
x = 35 + y
35+y = 5 + 3y
30 = 2y
y = 15
x = 35 + 15 = 50

The larger number is equal to 50


#3
42 different one topping sundaes. 7 flavors of ice-cream, and x types of toppings. We know through basic combinatronical rules that 7x = 42. Therefore, x = 6.

Answer 2

Step 1: Simplify both sides of the equation. 7−(2x+11)+3(3−x)=20 Simplify: (Hide steps) 7+−2x+−11+(3)(3)+(3)(−x)=20(Distribute) 7+−2x+−11+9+−3x=20 (−2x+−3x)+(7+−11+9)=20(Combine Like Terms) −5x+5=20 −5x+5=20 Step 2: Subtract 5 from both sides. −5x+5−5=20−5 −5x=15 Step 3: Divide both sides by -5. −5x −5 = 15 −5 x=−3 3y+5 = x x-y = 35 x = 35+y 3y+5 = 35+y 3y-y = 30 y = 30/2 = 15 . x = 35+15 =50 7*6=42 So there are 6 toppings.