Question

write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. felipe and his workout partner are lifting weights together, doing many sets of each exercise. on a certain exercise, felipe is using a 41 - pound bar, increasing the amount of weight he lifts by 9 pounds on each set. his partner, meanwhile, started out using a 43 - pound bar and is upping the weight by adding 7 pounds on every set. eventually, felipe and his workout partner will be lifting the same amount, and will take turns using the same barbell. how many sets will they have completed? how much weight will they be lifting then? after completing sets, they will both be lifting pounds.

Explanation:

Step1: Define the equations

Let $x$ be the number of sets. Felipe's weight $y_1 = 41+9x$, his partner's weight $y_2=43 + 7x$. When they lift the same weight, $y_1=y_2$, so the system of equations is

$$\begin{cases}y = 41+9x\\y=43 + 7x\end{cases}$$

Step2: Substitute and solve for $x$

Since $41+9x=43 + 7x$, subtract $7x$ from both sides: $41+9x-7x=43 + 7x-7x$, which simplifies to $41 + 2x=43$. Then subtract 41 from both sides: $2x=43 - 41$, so $2x=2$. Divide both sides by 2: $x = 1$.

Step3: Find the weight

Substitute $x = 1$ into either of the original equations. Using $y=41+9x$, we get $y=41+9\times1=50$.

Answer:

After completing 1 sets, they will both be lifting 50 pounds.