Question

Kate makes a donation to a charitable organization on a monthly basis. Her monthly donation is directly proportional to the square of her monthly savings. If she saves $900 and $1200 in January and February respectively, her donation increases by $35 from January to February. Find the amount of money she donates to the charitable organization in each of the two months.

Answer 1

Kate's donations to the charitable organization were $45 in January and $80 in February, calculated by solving a proportionality problem involving her monthly savings and donations.

Step-by-step explanation:

We're given that Kate's monthly donation is directly proportional to the square of her monthly savings. Let's denote her savings by S, her donation by D, and the constant of proportionality by k. The relationship can be expressed as D = kS^2.

For January, with savings of $900, the donation would be D1 = k(900)^2. For February, with savings of $1200, the donation would be D2 = k(1200)^2. We are told the increase in donation is $35. Thus, D2 - D1 = $35. Substituting the equations for D1 and D2, we have k(1200)^2 - k(900)^2 = $35.

To solve for k:

• k(1200)^2 - k(900)^2 = $35
• k(1440000 - 810000) = $35
• k(630000) = $35
• k = $35 / 630000 = 1/18000

Now we calculate the donations:

• January donation: D1 = k(900)^2 = 1/18000 * 810000 = $45
• February donation: D2 = k(1200)^2 = 1/18000 * 1440000 = $80

Kate's donations for January and February were $45 and $80, respectively.