Question

Solve a system of equations using elimination: word problems NHRWrite a system of equations to describe the situation below, solve using elimination, and fill inthe blanks.An online boutique is having a special on personalized baby items. On Monday, they sold 24personalized baby blankets and 17 personalized hooded towels, for a total of $1,112 inreceipts. The following day, they received orders for 2 personalized baby blankets and 17personalized hooded towels, which brought in a total of $342. How much does each item sellfor?Blankets sell for $apiece, and hooded towels sell for $apiece.Submit

Answer 1

Given data:

Assume b = price of each blankets, and t = price of each towels.

Monday: 24b + 17t = $1,112

Tuesday: 2b + 17t = $342

Find: the price of each blanket and towels

Solution:

We can solve the system of equation above using elimination method.

First, we will subtract the two equations.

24b + 17t = $1,112

2b + 17t = $342

24b - 2b = 22b

17t - 17t = 0

1, 112 - 342 = $770

Therefore, we have the new equation:

$\begin{gathered} 22b=770 \\ \text{Divide both sides by 22.} \\ \frac{22b}{22}=\frac{770}{22} \\ b=35 \end{gathered}$

From the new equation 22b = 770, we were able to solve the price of each blanket and that is $35.

To solve for the price of the hooded towels, we can use either equation 1 or 2 and replace "b" with 35.

$\begin{gathered} 2b+17t=342 \\ 2(35)+17t=342 \\ 70+17t=342 \\ \text{Subtract 70 on both sides.} \\ 70+17t-70=342-70 \\ 17t=272 \\ \text{Divide both sides by 17.} \\ \frac{17t}{17}=\frac{272}{17} \\ t=16 \end{gathered}$

Therefore, t = 16, hence the price of each hooded towel is $16.

To summarize:

price of each personalized baby blanket = $35

price of each personalized baby towel = $16