trying to solve( 1.7f +1.3s=37.9)

      and            ( 5.6f +5.4s=147.2)
in Algebra 1 Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Problem: 1.7f + 1.3s+37.9 and 5.6f + 5.4s=147.2
trying to solve( 1.7f +1.3s=37.9)
      and            ( 5.6f +5.4s=147.2)

This is a system of two equations in two unknowns. There
is a specific process for handling these problems.

1.7f + 1.3s =  37.9
5.6f + 5.4s = 147.2

Let's eliminate all the decimal values by multiplying
everything by 10.

1) 17f + 13s =  379
2) 56f + 54s = 1472

The first thing we want to do is eliminate one of
the unknowns, either the f or the s. We do that by
getting the co-efficients in both equations to the
same value for one of the unknowns. It would be great
if the co-efficient in one equation were a multiple of
the co-efficient in the other equation, but that isn't
the case here. So, let's choose to eliminate the s by
multiplying equation 1 by 54 and multiplying equation
2 by 13.

54 * (17f + 13s) =  379 * 54
3) 918f + 702s = 20466

13 * (56f + 54s) = 1472 * 13
4) 728f + 702s = 19136

This allows us to subtract equation 4 from equation 3.

   918f + 702s = 20466
-(728f + 702s = 19136)
  ----------------------------
  190f             = 1330
190f = 1330
190f/190 = 1330/190
f = 7

We use that value for f in one of the original equations
to solve for s. Use equation 1.

17f + 13s =  379
17(7) + 13s =  379
119 + 13s = 379
119 + 13s - 119 = 379 - 119
13s = 260
13s/13 = 260/13
s = 20

We verify both values by using them in the other equation.

56f + 54s = 1472
56(7) + 54(20) = 1472
392 + 1080 = 1472
1472 = 1472

Answer: f = 7, s = 20

 

by Level 11 User (78.4k points)

Related questions

1 answer
asked Aug 12, 2013 in Algebra 1 Answers by banana! | 109 views
1 answer
asked Jul 16, 2013 in Algebra 1 Answers by anonymous | 270 views
1 answer
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
84,343 questions
89,142 answers
1,987 comments
7,327 users