After an exercise, Ali and Ben measured their heart rates. The ratio of their heart rates was 15:17 Bens heart beats 18 times per minute more than Ali. Calculate Ali heart rate

Step-by-step explanation:

Alis heart rate is 135 beats per minute

Let

x > Ali's heart rate

y > Ben's heart rate

we know that

\frac{x}{y}=\frac{15}{17}

y

x

=

17

15

isolate the variable x

x=\frac{15}{17}yx=

17

15

y > equation A

we have

y=x+18y=x+18 ---> equation B

Solve the system by substitution

substitute equation B in equation A

x=\frac{15}{17}(x+18)x=

17

15

(x+18)

Solve for x

x-\frac{15}{17}x=\frac{15}{17}(18)x−

17

15

x=

17

15

(18)

\frac{2}{17}x=\frac{270}{17}

17

2

x=

17

270

simplify

\begin{gathered}2x=270\\x=135\ beats\ per\ minute\end{gathered}

2x=270

x=135 beats per minute

therefore

Ali's heart rate is 135 beats per minute