Question 1152216: Kate makes a donation to a charitable organisation on a monthly basis. Her monthly donation is directly proportional to her monthy savings. If she saves $900 and $1200 in January ano February respectively,her donation increases by $35 from January to February. Find the amount of money she donates to the charitable organisation in each of the two months.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! d = donation
s = savings.
in january, savings = 900.
in february, savings = 1200.
in january, donation = d
in february donation = d + 35
since they are directly proportional, you get:
d / 900 = (d + 35) / 1200
cross multiply to get:
d * 1200 = 900 * (d + 35)
simplify to get:
d * 1200 = 900 * d + 35 * 900
subtract 900 * d from both sides of the equation and simplify to get:
300 * d = 31500
solve for d to get:
d = 31500 / 300 = 105
d + 35 is therefore equal to 140
you get:
d / 900 = (d + 35) / 1200 becomes 105 / 900 = 140 / 1200.
cross multiply to get:
105 * 1200 = 900 * 140
simplify to get:
126000 = 126000.
this confirms that her monthly donation is directly proportional to her savings.
the ratio in january is 105 / 900 =
the amount of money that she donates to the charitable organization in each of the two months is 105 in january and 140 in february.
you can also confirm this by using the directly porportional formula of y = k * x
when x = 105, y = 900
solve for k to get k = 900 / 105 = 8.571428571.
when x = 140, y = k * 140 = 8.571428i571 * 140 = 1200.
your solution is that she donates 105 in january and 140 in february to the charitable organization.
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