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Question 1143247: The ratio of how many peas Julia has to how many peas Vlada has was 3:2. After Julia gave Vlada 15 peas, she still had 10 more peas than Vlada. How many peas did Julia have at first?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! j = number of peas that julia has.
v = number of peas that vlada has.
j/v = 3/2
solve for j to get j = 3/2 * v
after julia gave vlada 15 peas, julia still had 10 more peas than vlada.
equation for that is:
j - 15 = (v + 15) + 10.
combine like terms to get j - 15 = v + 25.
add 15 to both sides of this equation to get j = v + 25 + 15.
combine like terms to get j = v + 40.
in the equation of j = 3/2 * v, replace j with v + 40 to get v + 40 = 3/2 * v.
subtract v from both sides of this equation to get 40 = 3/2 * v - v
simplify to get 40 = 1/2 * v
multiply both sides of this equation by 2 and solve for v to get v = 80.
you have v = 80
you have j = 3/2 * v.
replace v with 80 to get j = 3/2 * 80
solve for j to get j = 120.
you have j = 120 and v = 80
j/v = 120/80 = 3/2, which confirms the original ratio is correct.
julia had 120 peas at first.
this is your solution.
to confirm the rest of the probelm, julia gives vlada 15 peas.
now julia has 105 and vlada has 95.
julia still has 10 more peas than vlada.
the rest of the problem is confirmed to be true.
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