Question

Last week, a dairy farm produced m kg of cheese. The dairy farm also produced 28 kg more yoghurt than cheese and 3 times as much ice cream as cheese. The dairy farm produced more kilograms of ice cream than yoghurt last week. Write and solve an inequality to work out the possible values of m.​

Answer 1

To work out the possible values of m, set up inequalities based on the given information. Simplify the inequality to find that m > 14.

Step-by-step explanation:

To work out the possible values of m, we need to set up inequalities based on the given information:

• The dairy farm produced 28 kg more yoghurt than cheese, so the amount of yogurt produced can be expressed as m + 28.
• The dairy farm produced 3 times as much ice cream as cheese, so the amount of ice cream produced can be expressed as 3m.
• The dairy farm produced more kilograms of ice cream than yogurt, so 3m > m + 28.

Simplifying the inequality, we have 3m > m + 28. Subtracting m from both sides, we get 2m > 28. Finally, dividing both sides by 2, we find that m > 14. This means that the possible values of m are any number greater than 14.

Answer 2

Hence the possible values of m are m > 14

So, the dairy farm produced greater than 14 kg of cheese

Step-by-step explanation:

We have m = kg of cheese,

let y = yogurt

and i = ice cream,

The dairy farm also produced 28 kg more yoghurt than cheese

y = m + 28

3 times as much ice cream as cheese

i = 3m

The dairy farm produced more kilograms of ice cream than yoghurt last week

i > y

so we have,

y = m + 28 (i)

i = 3m (ii)

i > y (iii)

Now, using (i) and (ii) in (iii),

i > y

3m > m + 28 (i = 3m, y = m + 28)

subtracting m from both sides,

3m - m > m - m + 28

2m > 28

dividing by 2 on both sides,

m > 28/2

m > 14