how to solve word problems

Question

To buy both a new car and a new house, Tina sought two loans totaling $318,338.

The simple interst rate loan on the first loan was2.4%, while the simple intrest rate on the second loan was4.7%. At the end of the first year Tina paid a combined intrest payment of $14,761.81. What were the amounts of the two loans?

Answer 1

Problem: how to solve word problems
To buy both a new car and a new house, Tina sought two loans totaling $318,338.
The simple interst rate loan on the first loan was2.4%, while the simple intrest
rate on the second loan was4.7%. At the end of the first year Tina paid a combined
intrest payment of $14,761.81. What were the amounts of the two loans?

The two loans are x and (318338 - x)
The interest on the first loan was 0.024x
The interest on the second loan was 0.047(318338 - x)
The total interest was 0.024x + 0.047(318338 - x) = 14761.81

0.024x + 0.047(318338 - x) = 14761.81
0.024x + 14961.89 - 0.047x = 14761.81
-0.023x + 14961.89 = 14761.81
-0.023x + 14961.89 - 14961.89 = 14761.81 - 14961.89
-0.023x = -200.08
-0.023x/-0.023 = -200.08/-0.023
x = 8699.13

The first loan, for the car, was $8,699.13
The second loan, for the house, was $309,638.87