Question

a company plans to build at least 152 igloos in a single week by employing skilled workers from the cities of tomsk and kyzyl. all tomskians build the same number of igloos per week, and all kyzylians build the same number of igloos per week.
let t represent the number of tomskians and k represent the number of kyzylians the company needs to employ to meet its goal.
6t + 5k ≥ 152
according to the inequality, how many igloos does each tomskian build per week, and how many igloos does each kyzyl ian build per week?
each tomskian builds igloos per week, and each kyzylian builds igloos per week.
can the company achieve its goal by employing 10 tomskians and 19 kyzylians?
choose 1 answer:
a yes
b no

Explanation:

Part 1: Igloos per worker

Step1: Analyze the inequality structure

The inequality is \(6T + 5K\geq152\), where \(T\) is the number of Tomskians and \(K\) is the number of Kyzilians. The coefficient of \(T\) represents the number of igloos each Tomskian builds, and the coefficient of \(K\) represents the number of igloos each Kyzilian builds.

Step2: Identify the values

From \(6T+5K\geq152\), the coefficient of \(T\) is 6, so each Tomskian builds 6 igloos per week. The coefficient of \(K\) is 5, so each Kyzilian builds 5 igloos per week.

Step1: Substitute \(T = 10\) and \(K=19\) into the inequality

We substitute \(T = 10\) and \(K = 19\) into \(6T+5K\) to check if it is greater than or equal to 152.
\[

$$\begin{align*} 6T+5K&=6\times10 + 5\times19\\ &=60+95\\ &=155 \end{align*}$$

\]

Step2: Compare with 152

Since \(155\geq152\), the company can achieve its goal.

Answer:

(for first part):
Each Tomskian builds \(\boldsymbol{6}\) igloos per week, and each Kyzilian builds \(\boldsymbol{5}\) igloos per week.

Part 2: Can the company achieve the goal?