Let x represent the cost of one of Tanya's items. Since each item that Tony bought was $1.75 less than the items that Tanya bought, then x-1.75 represent the cost of one of Tony's items.
Tanya bought 5 items, each cost x, then the total amount is 5x.
Tony bought 6 items, each cost x-1.75, then the total amount is 6(x-1.75).
If both Tanya and Tony paid the same amount of money, then
(a) 5x=6(x-1.75).
Let's solve it:
(b) 5x=6x-10.5,
5x-6x=-10.5,
-x=-10.5,
x=10.5.
(c) Substitute x=10.5 into equation:
5·10.5=52.5,
6·(10.5-1.75)=6·8.75=52.5
52.5=52.5
(d) The individual cost of Tanya's items is $10.5 and the individual cost of Tony's items is $8.75.
Solution:
(a) Cost of one of Tanya's item: x
..., but each was $1.75 less than the items that Tanya bougth:
Cost of one of Tony's item: x-1.75
Tanya bought 5 items that each cost the same amount:
Tanya paid: Number of items bought * Cost of each item
Tanya paid=5x
Tony bought 6 items:
Tony paid: Number of items bought * Cost of each item
Tony paid=6*(x-1.75)
Both paid the same amount of money:
Tanya paid = Tony paid
5x=6*(x-1.75)
Answer: Write an equation: 5x=6*(x-1.75)
(b) Solve the equation
5x=6*(x-1.75)
Elminating the parentheses on the right side of the equation applying the distributive property:
5x=6*x-6*1.75
Multiplying:
5x=6x-10.5
Solving for x: Subtracting 6x both sides of the equation:
5x-6x=6x-10.5-6x
-x=-10.5
Multiplying both sides of the equation by -1:
(-1)*(-x)=(-1)*(-10.5)
x=10.5
What was the individual cost of each person's items:
Cost of one of Tanya's items: x=$10.5
Cost of one of Tony's items: x-$1.75=$10.5-$1.75=$8.75
(c) Check the solution:
Tanya paid: 5x=5($10.5)=$52.5
Tony paid: 6(x-$1.75)=6($10.5-$1.75)=6($8.75)=$52.5
Both paid the same amount of money
(d) State the solution in complete sentences:
Cost of one's Tanya's items is $10.5
Cost of one's Tony's items is $8.75
