Question

Zhao Xue wants to buy milk and yogurt. She wants to buy a total of at least 6.5 gallons of dairy products (condition A), and she has a budget of $20 (condition B). The graph represents the constraints on the number of gallons of milk M and yogurt Y Zhao Xue buys. Zhao Xue buys 4 gallons of milk. how many gallons of yogurt can she buy to meet both her constraints?
A.) Exactly 2.5 gallons
B.) At least 4 gallons and at most 6.5 gallons
C.) At least 2.5 gallons and at most 4 gallons
D.) Zhao Xue doesn’t have enough money left to buy any yofurt

Answer 1

Answer: The answer is (D). Zhao Xue doesn’t have enough money left to buy any yofurt

Step-by-step explanation:  Given that Zhao Xue is buying buy milk and yogurt, a total of at least 6.5 gallons of dairy products and she has a budget of $20. The given graph represents the constraints on the number of gallons of milk 'M' and yogurt 'Y' Zhao Xue buys. Zhao Xue buys 4 gallons of milk. We need to calculate the number of gallons of yogurt she can buy to meet both her constraints.

From the graph, we can write

Condition A :

$M+Y\geq 6.5.$

Condition B :

$8M+5Y\leq40.$

Now, if she buys 4 gallons of milk, the the conditions become

$4+Y\geq 6.5~~\Rightarrow Y\geq 2.5,\\\\8\times 4+5Y\leq 40~~\Rightarrow Y\leq 1.6.$

Here, there will be no solution to these constraints.

Therefore, she does not have enough money left to buy any yogurt.

Thus, the correct option is (D).

Answer 2

Answer: exactly 2.5 gallons

This is for khan academy.