# How construct simultaneous equations from worded problems?

##

Can someone please explain to me how to do question 17 and 14? Answer this and I will love you forever!

Can someone please explain to me how to do question 17 and 14? Answer this and I will love you forever!

##### 1 Answer

Problem 17 set up:

You are given that there are 3 types of tea.

Let x = the mass (in kilograms) of the tea for $10 per kilogram

Let y = the mass (in kilograms) of the tea for $11 per kilograms

Let z = the mass (in kilograms) of the tea for $12 per kilograms

The phrase "so as to obtain 100 kilograms" allows us to write equation [1]:

The phrase "100 kilograms worth $11.20 per kilograms" means that the blend will cost:

Please notice how the kilograms cancel:

The only remaining unit is dollars:

This allows us to write equation [2]:

The phrase "If the same amounts of the two higher prices teas are used" allows us to write equation [3]:

Here are your 3 linear equations:

Problem 14 setup:

Let x = the number of shirts

Let y = the number of ties

Selling everything for $10000 tells us that the right side of the equation [1] is $10000. The prices $100 for 3 shirts and $20 per tie tells us that the coefficients are

For the second equation, multiply x by

Simplify equation [2]:

Here are your two linear equations: