If 3s+5t = 10, and 2s-2=7, what is the value of 0.5s + 3t?

Hello,

let's start with cracking the two problems that already have an answer so we can understand how to solve 0,5s + 3t.

2s - 2 = 7

2s - 2 = 7 is an expression that says "the value of 2s minus 2 equals 7". That must mean that the original value of 2s was 9, because 7 plus 2 is 9.

That must mean that 1s equals 4.5, because 2s equals 9.

3s + 5t = 10

We then move on to the next problem, 3s + 5t = 10. We know that 1s equals 4.5, so 3s must equal 4.5 * 3 = 13.5. Wait a second, 13.5 is above 10! What is this!? Well, 5t must be a negative value, with a total value of (-3.5). We use brackets to make it easier to read negative values. It's easy then! 13.5 + (-3.5) = 10! Actually, not as easy as someone may think, negative numbers involve in a bunch of pesky rules, that's why the answer is 10 and not 17. I recommend you to read about said rules in case you already haven't.

So, 5t equals (-3.5). How much is 1t? Let's simply just take (-3.5) and divide it by 5, like this: (-3.5) / 5 = (-0.7). 1t equals (-0.7).

0.5s + 3t = ?

We now know that 1s equals 4.5 and that 1t equals (-0.7).

0.5s is half of the value of 1s. 0.5s = 4.5 / 2 = 2.25.

3t = (-0.7) * 3 = (-2.1).

A simple, readable, version of the problem would then be 2.25 + (-0.7).

2.25 + (-2.1) = 0.15

Finally, we have our answer, 0.5s + 3t = 0.15.

Hope this helped. Long answers scare me.

If 3s+5t = 10, and 2s-2=7, what is the value of 0.5s + 3t?

If 2s - 2 = 7     add 2 to both sides

2s = 9             divide both sides by 2

s = 9/2   and substituting this into 3s + 5t = 10 to find t, we have

3(9/2) +5t = 10

27/2 + 5t = 10      subtract 27/2 from both sides

5t = 10 - 27/2

5t = 20/2 - 27/2

5t =-7/2       divide both sides by 5

t = -7/10

And substituting these values into  .5s + 3t, we have

.5(9/2) + 3(-7/10) =

(1/2)(9/2) - 21/10 =

9/4 - 21/10  =

[90 - 84] / 40 =

6/40 =

3/20

2s-2=7

2s=9

s=4.5

3*4.5*5t=10

13.5*5t=10

5t=10/13.5

5t=0.74

t=0.148

$${\mathtt{0.5}}{\mathtt{\,\times\,}}{\mathtt{4.5}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{0.148}} = {\frac{{\mathtt{1\,347}}}{{\mathtt{500}}}} = {\mathtt{2.694}}$$

Chris can you check these answers and give the scores/comment please?

Anonymous who has just joined up and is now AlexM has asked me to look over his answer.   

Hi Alex, I will look at your answer now.  I have copied it here so I can look and give feedback  both at the same time.   

let's start with cracking the two problems that already have an answer so we can understand how to solve0,5s + 3t. 

2s - 2 = 7

2s - 2 = 7 is an expression that says "the value of 2s minus 2 equals 7". That must mean that the original value of 2s was9, because 7 plus 2 is 9.

That must mean that 1s equals 4.5, because 2s equals 9.     GOOD

 3s + 5t = 10

We then move on to the next problem, 3s + 5t = 10. We know that 1s equals 4.5, so 3s must equal 4.5 * 3 = 13.5. Wait a second, 13.5 is above 10! What is this!? Well, 5t must be a negative value, with a total value of (-3.5). We use brackets to make it easier to read negative values. It's easy then! 13.5 + (-3.5) = 10! Actually, not as easy as someone may think, negative numbers involve in a bunch of pesky rules, that's why the answer is 10 and not 17. I recommend you to read about said rules in case you already haven't.

So, 5t equals (-3.5). How much is 1t? Let's simply just take (-3.5) and divide it by 5, like this: (-3.5) / 5 = (-0.7). 1t equals(-0.7).         GOOD

0.5s + 3t = ?

We now know that 1s equals 4.5 and that 1t equals (-0.7).

0.5s is half of the value of 1s. 0.5s = 4.5 / 2 = 2.25.

3t = (-0.7) * 3 = (-2.1).

 A simple, readable, version of the problem would then be 2.25 + (-0.7).

2.25 + (-2.1) = 0.15

 Finally, we have our answer, 0.5s + 3t = 0.15.       (YES this is the sames as CPhill's answer.)

 You have answered well Alex,  thank you.