A racket and 4 shuttlecocks cost $13. The racket costs $5.50 more than shuttlecock. Find cost of a shuttlecock

"A racket and 4 shuttlecocks cost $13."





r + 4s = $13





"The racket costs $5.50 more than shuttlecock."





r = s + $5.50





Substitute in the first equation:





(s + $5.50) + 4s = $13.00





5s = $7.50





s = $1.50





So a shuttlecock costs $1.50. And then, even tho the problem doesn't ask for it:





r = $1.50 + $5.50 = $7





A racket costs $7.|||let r be the racket and s be the shuttlecock





r + 4s = 13


r = s + 5.5





(s + 5.50) + 4s = 13 (substitute)





5s + 5.50 = 13 (combine like terms)


- 5.50 -5.50





5s = 7.50


/5 /5 divide by 5 to get s by itself





s = $1.50





r = s + 5.50





r = 1.50 + 5.50


r = $7





shuttlecocks are $1.50 each($6 for 4) and the racket is $7, which would total $13.





Look in the index of your book under "Systems of Equations" or "Equations - Systems of", then look for "Substitution".|||If all five pieces cost $13, then say that the r = racket and s = shuttlecock





So, r + 4s = 13


and, if the racket is $5.50 more than one shuttlecock,


then r = s + 5.5





Substitue the second equation into the first because it is already solved for one variable (r):


s + 5.5 + 4s = 13


5s + 5.5 = 13


5s = 13 - 5.5 = 7.5


s = 7.5 / 5 = 1.5





So, the shuttlecocks each cost $1.50 and the racket is $7.00|||let r=racket


s=shuttlecock





r+4s=13


r=5.50+s





(5.50+s)+4s=13


4s=13-(5.5+s)


4s=13-5.5-s


s+4s=13-5.5


5s=7.5


s=1.5





to check


r=5.5+s


r=5.5+1.5


r=7





r+4s=13


7+4(1.5)=13


7+6=13


13=13|||R+4S=13


R= S+5.50 so going to the first 5S +5.50=13 ==%26gt;5S = 7,50 and





S=1.50 R=7.00