Question

At a bargain store. Tanya bought 5 items that each cost the same amount. Tony bought 6 items that each cost the same amount, but each was $1.75 less than the items that Tanya bought. Both Tanya and Tony paid the same amount of money. What was the individual cost of each person's items?
(a) Write an equation. Let x represent the cost of one of Tanya's items.
(b) solve the equation. show your work
(c) check the solution. show your work
(d) State the solution in complete sentences

I have no idea how to do this ..please explain..thanks

Answer 1

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

Answer 2

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.