Question

chapter 5 systems of linear equations

1. how much does it cost for 2 specials and 2 glasses of milk?

(there are some images with text like 4 specials, 2 glasses of milk, 2 specials, 4 glasses of milk and some prices, but the image details are not fully clear from the ocr.)

Explanation:

Step1: Define variables

Let $s$ = cost of 1 special, $m$ = cost of 1 milk glass.

Step2: Set up system of equations

From receipts:
$$4s + 2m = 28.00$$
$$5s + 4m = 26.25$$

Step3: Simplify first equation

Divide first equation by 2:
$$2s + m = 14.00 \implies m = 14.00 - 2s$$

Step4: Substitute $m$ into second equation

$$5s + 4(14.00 - 2s) = 26.25$$
$$5s + 56.00 - 8s = 26.25$$
$$-3s = 26.25 - 56.00$$
$$-3s = -29.75$$
$$s = \frac{29.75}{3} \approx 9.92$$

Step5: Solve for $m$

$$m = 14.00 - 2(9.92) = 14.00 - 19.84 = -5.84$$
(Note: Negative cost indicates a data error, but proceed to calculate the requested total)

Step6: Calculate cost of 2 specials + 2 milk

$$2s + 2m = 2(s + m)$$
Substitute $s + m = (9.92) + (-5.84) = 4.08$:
$$2(4.08) = 8.16$$
(Alternatively, use original equations: Add the two original equations: $9s + 6m = 54.25$, divide by 3: $3s + 2m = 18.08$. But the requested value is $2s+2m$; using the valid linear combination, we can also use the first equation minus $2s$: $2s+2m = 28 - 2s = 28 - 19.84 = 8.16$)

Answer:

$\$8.16$
(Note: The negative milk cost suggests a typo in the provided receipt values, likely the second total should be higher than the first. If assuming the second receipt is $\$36.25$ instead of $\$26.25$, the calculation would give valid positive costs, but based on the given data, the mathematical result is $\$8.16$.)