Brain Teasers
Antique Jewelry
Three pieces of antique jewelry - a locket, a pin, and a ring - have ages whose sum is 310 years. The sum of 2 times the age of the locket 5 years ago and the age of the pin 10 years ago is 240 years. The difference between 3 times the locket's age in 3 years and 2 times the ring's age 4 years ago is 0. Find the ages of the locket, the pin, and the ring.
Hint
The equation system is one of three open sentences each having three placeholders.Answer
Locket=LPin=P
Ring=R
L+P+R=310 (equation 1)
2L+P=260 (equation 2)
3L-2R=-17 (equation 3)
Combine equations 1 and 2, and multiply equation 2 by -1.
L+P+R=310
-2L-P=-260
____________
-L+R=50
Now multiply the new equation by 2 and combine it with equation 3.
3L-2R=-17
-2L+2R=100
____________
L=83
So the locket is 83 years old.
Now substitute the value for "L" into the original equation 2.
2L+P=260
2(83)+P=260
166+P=260
P=94
So the pin is 94 years old.
For the final step substitute the locket's age into the original equation 3 to get the ring's age.
3L-2R=-17
3(83)-2R=-17
249-2R=-17
R=133
So the ring is 133 years old.
Add the three values to verify:
83+94+133=310
Hide Hint Show Hint Hide Answer Show Answer
What Next?
View a Similar Brain Teaser...
If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.
Solve a Puzzle
Comments hidden to avoid spoilers.
Follow Braingle!