Three pieces of antique jewellery – 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=L
Pin=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 age of the locket’s age into the original equation 3 to get the age of the ring.
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
