In a video game green gems are worth 5 points and blue gems are worth 10 points. Eric collects 25 gems and earned 160?points form his gems. Find how many green gems and how many blue gems Eric collected.

Accepted Solution

Eric collected 18 green gems and 7 blue gems.Step-by-step explanation:Let, Green gems = xBlue gems = yOne green gem = 5 pointsOne blue gem = 10 pointsAccording to given statement; x+y=25   Eqn 15x+10y=160   Eqn 2Multiplying Eqn 1 by 5;[tex]5(x+y=25)\\5x+5y=125\ \ \ Eqn\ 3[/tex]Subtracting Eqn 3 from Eqn 2;[tex](5x+10y)-(5x-5y)=160-125\\5x+10y-5x-5y=35\\5y=35[/tex]Dividing both sides by 5;[tex]\frac{5y}{5}=\frac{35}{5}\\y=7[/tex]Putting y=7 in Eqn 1;[tex]x+7=25\\x=25-7\\x=18[/tex]Eric collected 18 green gems and 7 blue gems.Keywords: linear equations, subtractionLearn more about linear equations at:brainly.com/question/4168505brainly.com/question/4228574#LearnwithBrainly