A household's monthly utility bill is calculated by summing up the charges it incurs for its usage of electricity, gas and water based on the prevailing price rate per unit. The table below shows Mrs Ang's household utilities usage for the months of April, May, June and July in a particular year.

	Monthly usage (units)
	April	May	June	July
Electricity	23	33	49	35
Gas	12	16	22	17
Water	16	21	33	26

The prevailing price rate per unit were unchanged for the period of April to June. However, in the month of July, the electricity rate was increased by 7%, the gas rate was reduced by 5% and the water rate remained unchanged. Given that Mrs Ang's monthly utility bills for April, May and June were $103.00, $142.00 and $209.00 respectively, find her monthly utility bill for the month of July.

1. Formulate a system of linear equations based on the data provided for April, May, and June.

Let $x$, $y$, and $z$ be the price per unit (in $) of electricity, gas, and water respectively.
We form the following system of linear equations from the table and given monthly bills:

2. Solve the system of equations using a graphing calculator.

Using a graphing calculator to solve the system, we obtain the unit prices:
$x = 2.2$
$y = 2.5$
$z = 1.4$

3. Calculate the revised unit prices for July.

Applying the percentage changes for the month of July, the new rates are:
Electricity: $2.20 \times (1 + 0.07) = \char36{}2.354$
Gas: $2.50 \times (1 - 0.05) = \char36{}2.375$
Water: $\char36{}1.40$ (remains unchanged)

4. Calculate the total utility bill for July and round appropriately.

Total bill for July
$= 35(2.354) + 17(2.375) + 26(1.40)$
$= 82.39 + 40.375 + 36.40$
$= 159.165$
$\approx \char36{}159.17$ (to 2 d.p. as it is a monetary value)