Solving ratios and substitution Problems

Question

Hello! I found a way to solve ratios online but it seemed to have failed on another problem. Please help by explaining a method that works for all. Here is an example problem:

The ratio of t to r is 17:11, the total is 3444. What is t? 

 

And then a substitution problem:

p+d=50

5P+10d=140

 

I rearranged the first equation to p=50-d and plugged it into the second one. I got d=-22, plugged that into the original first equation and got p=72.

It appearantly is wrong. I must check the book again to make sure of some things, but meanwhile please help.

 

Answer 1

t : r = 17 : 11 means that for each of 28 (17 + 11) parts is split into subgroups of 17 and 11.

 

How many groups of 28 are in 3444?

 

3444 / 28 = 123

 

So there are 123 subgroups of 17, or 2091, and

123 subgroups of 11, or 1353

 

Check:

 

1352 + 2091

3444

 

5(50 - d) + 10d = 140               distribute

250 - 5d + 10d = 140                combine like terms

250 + 5d = 140                         subtract 250 from both sides

5d = -110                                   divide both sides by 5

d = -22

p = 72

 

Check

5(72) + 10(-22) = 140

360 - 220 = 140