Question

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 \( \boxed{32} \).