SOLUTION: How do I go about solving this ratio problem? Jay and Raymond bought some cookies in the ratio 3:5. After Raymond bought another 24 cookies, the ratio became 1:2. How many cooki

Question 1119941: How do I go about solving this ratio problem?
Jay and Raymond bought some cookies in the ratio 3:5. After Raymond bought another 24 cookies, the ratio became 1:2. How many cookies did Jay buy?
Thanks in advance.
Found 3 solutions by Theo, ikleyn, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
j is the number of cookies that jay has.
r is the number of cookies that raymond has.

the ratio of the number of jay's cookies to raymond's cookies is 3/5.

you get:

j/r = 3/5

when raymond buys another 24 cookies, the ratio becomes 1/2.

you get:

j/(r+24) = 1/2.

you have:

j/r = 3/5.

j/(r+24) = 1/2

these 2 equations need to be solved simultaneously.

multiply both sides of the first equation by 5r to get:

j/r = 3/5 becomes 5j = 3r.

subtract 3r from both sides of this equation to get:

5j - 3r = 0

multiply both sides of the second equation by 2 * (r+24) to get:

j/(r+24) = 1/2 becomes 2j = r+24

subtract r from both sides of this equation to get:

2j - r = 24

the two equations that need to be solved simultaneously are now:

5j - 3r = 0
2j - r = 24

multiply both sides of the second equation by 3 and leave the first equation as is to get:

5j - 3r = 0
6j - 3r = 72

subtract the first equation from the second to get:

j = 72

go back to the first original equation of j/r = 3/5 and replace j with 72 to get:

j/r = 3/5 becomes 72/r = 3/5

solve for r to get r = 72 * 5 / 3 = 120.

you now have:

j = 72
r = 120

j/r = 72 / 120.

divide numerator and denominator of this equation by 24 to get:

j/r = 3/5.

first ratio is correct when j = 72 and r = 120.

second original equation is j/(r+24) = 1/2.

replace j with 72 and r with 120 to get:

72/(120 + 24) = 1/2 becomes 72/144 = 1/2 which becomes 1/2 = 1/2 when 72/144 numerator and denominator are both divided by 72.

solution looks good.

number of cookies that jay had originally are 72.

number of cookies that raymond had originally are 120.

solution is jay bought 72 cookies.

another way to solve this is as shown below.

2 original equations are:

j/r = 3/5.
j/(r+24) = 1/2

solve for j in both equations to get:

j = 3/5 * r
j = 1/2 * (r + 24)

simplify to get:

j = 3/5 * r
j = 1/2 * r + 1/2 * 24

simplify further to get:

j = 3/5 * r
j = 1/2 * r + 12

since j is equal to both, then both are equal to each other and you get:

3/5 * r = 1/2 * r + 12

subtract 1/2 * r from both sides of this equation to get:

3/5 * r - 1/2 * r = 12

multiply both sides of this equation by 10 to get:

6 * r - 5 * r = 120

solve for r to get:

r = 120

go back to the first original equation and replace r with 120 to get:

j/r = 3/5 becomes j/120 = 3/5

solve for j to get j = 120 * 3/5 = 24 * 3 = 72

you get j = 72 and r = 120; this is the same answer as before, just derived in a different way.

Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.

Jay had 3x cookies, Raymond had 5x. After Raymond bought another 24 cookies, = ====> 6x = 5x + 24 ====> 6x - 5x = 24 ====> x = 24. Answer. Jay originally had 3x = 3*24 = 72 cookies.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

How do I go about solving this ratio problem?
Jay and Raymond bought some cookies in the ratio 3:5. After Raymond bought another 24 cookies, the ratio became 1:2. How many cookies did Jay buy?
Thanks in advance.

Let the multiplicative factor be x
Then Jay bought 3x and Raymond, 5x cookies
Since Raymond bought 24 more, and the ratio became 1:2, we get:
6x = 5x + 24 ------- Cross-multiplying
x = 24
Therefore, Jay bought
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