Two babies were born on the same day. One of them weighed three kilograms and the other 3.6 kilograms. Per week, the first baby gained 190 grams and the other gained 140 grams. At what age in weeks will they weigh the same?
When the first baby was born, it weighed three kilograms. This is equal to 3000 grams, as there are 1000 grams in one kilogram. This baby increased in weight by 190 grams per week. The second baby weighed 3.6 kilograms when born. This is equal to 3600 grams. The second baby increased in weight by 140 grams per week.
If we let 𝑥 be the number of weeks when the weights of the two babies are equal, we can set up a linear equation. The weight of baby one is given by the expression 3000 plus 190𝑥. And the weight of baby two is given by the expression 3600 plus 140𝑥. We want to calculate 𝑥 when these two expressions are equal.
Subtracting 140𝑥 from both sides of the equation gives us 3000 plus 50𝑥 is equal to 3600. Subtracting 3000 from both sides of this new equation gives us 50𝑥 is equal to 600, as 3600 minus 3000 is equal to 600. Finally, dividing both sides by 50 gives us a value for 𝑥 equal to 12. We can therefore say that the two babies will weigh the same after 12 weeks. After 12 weeks, both babies will weigh 5280 grams.