Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Aditi is participating in a walkathon fundraiser. Two anonymous donors agree to donate money according to the distance she walks. The money, 
A, in dollars, that she receives from the first donor for walking 
d kilometers is given by the formula 
A(d)=12 d. The total money, 
T, in dollars, that she receives from both donors for walking 
d kilometers is given by the formula 
T(d)=d^(2)+20 d.
Let 
B be the money that Aditi receives from the second donor for walking 
d kilometers.
Write a formula for 
B(d) in terms of 
A(d) and 
T(d).

B(d)=
Write a formula for 
B(d) in terms of 
d.

Aditi is participating in a walkathon fundraiser. Two anonymous donors agree to donate money according to the distance she walks. The money, A A , in dollars, that she receives from the first donor for walking d d kilometers is given by the formula A(d)=12d A(d)=12 d . The total money, T T , in dollars, that she receives from both donors for walking d d kilometers is given by the formula T(d)=d2+20d T(d)=d^{2}+20 d .\newlineLet B B be the money that Aditi receives from the second donor for walking d d kilometers.\newlineWrite a formula for B(d) B(d) in terms of A(d) A(d) and d d 00.\newlineB(d)= B(d)= \newlineWrite a formula for B(d) B(d) in terms of d d .\newlineB(d)= B(d)=\square

Full solution

Q. Aditi is participating in a walkathon fundraiser. Two anonymous donors agree to donate money according to the distance she walks. The money, A A , in dollars, that she receives from the first donor for walking d d kilometers is given by the formula A(d)=12d A(d)=12 d . The total money, T T , in dollars, that she receives from both donors for walking d d kilometers is given by the formula T(d)=d2+20d T(d)=d^{2}+20 d .\newlineLet B B be the money that Aditi receives from the second donor for walking d d kilometers.\newlineWrite a formula for B(d) B(d) in terms of A(d) A(d) and d d 00.\newlineB(d)= B(d)= \newlineWrite a formula for B(d) B(d) in terms of d d .\newlineB(d)= B(d)=\square
  1. Given Formulas: We are given two formulas:\newline11. A(d)=12dA(d) = 12d, which represents the money Aditi receives from the first donor for walking dd kilometers.\newline22. T(d)=d2+20dT(d) = d^2 + 20d, which represents the total money Aditi receives from both donors for walking dd kilometers.\newlineWe need to find the formula for B(d)B(d), which represents the money Aditi receives from the second donor for walking dd kilometers.\newlineTo find B(d)B(d), we subtract A(d)A(d) from T(d)T(d) because B(d)B(d) is the difference between the total amount received and the amount received from the first donor.
  2. Finding B(d)B(d): Let's perform the subtraction:\newlineB(d)=T(d)A(d)B(d) = T(d) - A(d)\newlineB(d)=(d2+20d)(12d)B(d) = (d^2 + 20d) - (12d)\newlineNow, we simplify the expression by combining like terms.
  3. Performing Subtraction: After simplifying, we get:\newlineB(d)=d2+20d12dB(d) = d^2 + 20d - 12d\newlineB(d)=d2+8dB(d) = d^2 + 8d\newlineThis is the formula for B(d)B(d) in terms of dd.

More problems from Interpret parts of quadratic expressions: word problems