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Sandra has some lemon and peppermint sweets in a container. After she adds in 10 lemon sweets, 3/5 of the sweets are peppermint. After she adds in another 30 peppermint sweets, 3/4 of the sweets are peppermint. How many sweets does she have in the container in the end?

 Sep 20, 2021
edited by Guest  Sep 20, 2021
 #1
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How many sweets does sandra have in the container in the end?

 

Hello Guest!

 

\(\color{blue}z+p+10=\frac{2}{3}(z+p+10)+z\\ p+10=\frac{2}{3}z+\frac{2}{3}p+\frac{20}{3}\\ \frac{p}{3}=\frac{2z}{3}+\frac{20}{3}\)

\(p=2z+20\)

\( \color{blue}z+p+10+30=\frac{3}{4}(z+p+40)+z\\ p+40=\frac{3}{4}z+\frac{3}{4}p+30\\ \frac{p}{4}=\frac{3}{4}z-10\)

\(p=3z-40 \)

\(2z+20=3z-40\)

\(z=60\)

\(p=2z+20\)

\(p=140\)

 

\(140+10+30+60=\color{blue}240\ sweets\\ does\ Sandra\ have\ in\ the\ container\ in\ the\ end.\)

 

laugh  !

 Sep 21, 2021
edited by asinus  Sep 21, 2021
edited by asinus  Sep 21, 2021
 #2
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240 / 60 = 40 + 30 = 70 + 10 = 80

Guest Sep 21, 2021

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