MHB Algebra word problem solve for x

[Kiwiman]

Help me solve this word problem please & explain how you did it-thanks so much, I 'm tearing my hair out.

Jason purchased a can of tomato sauce and three pounds of apples for $\$7.05$. Gina purchased a can of tomato sauce and 5 pounds of apples for $\$11.35$. What is the price of the tomato sauce?

 

[anemone]

Hi Kiwiman! Welcome to MHB!

First, we let $T$ to represent the price of a can of tomato sauce and $A$ to represent the price of one pound of apples.

The first statement of the problem can be translated into a mathematical equation, which is

$T+3A=\$ 7.05$

and the second statement of the problem can be translated into another mathematical equation, i.e.

$T+5A=\$ 11.35$

If we subtract the second equation from the first equation, we get

$T+5A-(T+3A)=\$ 11.35-\$ 7.05\\T+5A-T-3A=\$ 4.30\\2A=\$ 4.30 \\A=\$ 2.15$

Once we get the value of $A$, can you tell me what should we do to find the value of $T$?

 

[HallsofIvy]

Do you understand that "helping you solve a problem" and "explaining how I solved the problem" are completely different things?

 

[Jameson]

50/50 we hear back from this user. Would love to be proven wrong. I hope this teasing gets a reply.

Why do you want an answer so badly, @Kiwiman ? Wouldn't you prefer to know how to do it from now on feel more confident about math? :)

 

[HallsofIvy]

Help me solve this word problem please & explain how you did it-thanks so much, I 'm tearing my hair out.

Jason purchased a can of tomato sauce and three pounds of apples for $\$7.05$. Gina purchased a can of tomato sauce and 5 pounds of apples for $\$11.35$. What is the price of the tomato sauce?

Let T be the cost of a can of tomato sauce and A the cost of a pound of apples. Then "a can of tomato sauce and 5 pounds of apples" cost T+ 5A= 11.35 and "a can of tomato sauce and 3 pounds of apples" cost T+ 3A= 7.05.

Solve the two equations
T+ 5A= 11.35
T+ 3A= 7.05

I wonder what they intend to make with tomato sauce and apples!