At a store, Eva bought two shirts and five hats for 154.00$. Nicole bought three same shirts and four same hats for 168.00$. What is the price of each shirt?

Answer 1

Let the price of each shirt be \( s \) and the price of each hat be \( h \).

From the information given:

1. Eva bought 2 shirts and 5 hats for a total of 154.00: \[ 2s + 5h = 154 \]

2. Nicole bought 3 shirts and 4 hats for a total of 168.00: \[ 3s + 4h = 168 \]

Now we have the following system of equations:

1. \( 2s + 5h = 154 \) \tag{1}
2. \( 3s + 4h = 168 \) \tag{2}

To solve this system of equations, we can multiply equation (1) by 3 and equation (2) by 2 to eliminate \( s \):

From equation (1): \[ 3(2s + 5h) = 3(154) \implies 6s + 15h = 462 \tag{3} \]

From equation (2): \[ 2(3s + 4h) = 2(168) \implies 6s + 8h = 336 \tag{4} \]

Now we can subtract equation (4) from equation (3): \[ (6s + 15h) - (6s + 8h) = 462 - 336 \] This simplifies to: \[ 7h = 126 \]

Now, divide both sides by 7: \[ h = 18 \]

Now that we have the price of the hats, we can substitute \( h = 18 \) back into equation (1) to find \( s \): \[ 2s + 5(18) = 154 \] \[ 2s + 90 = 154 \] Subtract 90 from both sides: \[ 2s = 64 \] Now divide by 2: \[ s = 32 \]

Thus, the price of each shirt is \( \boxed{32} \).