Question

1. at a bargain store, tanya bought 3 items that each cost the same amount. tony bought 4 items that each cost the same amount, but each was $2.25 less than the items that tanya bought. both tanya and tony paid the same amount of money. what was the total amount that tanya and tony spent? write an equation. let x represent the cost of one of tanyas items.

Explanation:

Step1: Set up the cost - equation

Tanya bought 3 items at $x$ each, so she spent $3x$. Tony bought 4 items at $(x - 2.25)$ each, so he spent $4(x - 2.25)$. Since they spent the same amount, the equation is $3x=4(x - 2.25)$.

Step2: Solve the equation for $x$

Expand the right - hand side: $3x = 4x-9$.
Subtract $3x$ from both sides: $0=4x - 3x-9$.
Simplify to get $x = 9$.

Step3: Calculate the total amount they spent

Tanya spent $3x=3\times9 = 27$. Tony spent the same amount, 27.
The total amount they spent is $27 + 27=54$.

Answer:

54