Question

Neha is organising a weekend workshop and needs to print 200 brochures. She is considering two printing services: a nearby print shop and an online printing service. At the nearby print shop, each brochure will cost \$m with no additional costs. Each brochure will cost a bit less at \$n at the online service, but there's a flat setup fee of \$50. These are the only costs involved. Neha calculated that by choosing the online service over the print shop for 200 brochures, she would save exactly \$290. Select a value for m and n that are jointly consistent with the information provided. Make only two selections, one in each column.

Hint:

In problems that require finding values from a list, it's often most efficient to first derive a single equation relating the unknown variables. Then, systematically test the options against this simplified equation rather than performing the full calculation for every possible combination.

Answer 1

Step 1: Formulate the cost equations for each service. Let \(C_p\) be the total cost at the nearby print shop and \(C_o\) be the total cost at the online service.

Cost at Print Shop: \( C_p = 200 \times m \)
Cost at Online Service: \( C_o = (200 \times n) + 50 \)
Step 2: Use the information about the savings to create an equation. The savings from choosing the online service is the difference between the print shop cost and the online service cost. \[ \text{Savings} = C_p - C_o \] \[ 290 = (200m) - ((200n) + 50) \] Step 3: Solve the equation to find the relationship between m and n. \[ 290 = 200m - 200n - 50 \] \[ 290 + 50 = 200m - 200n \] \[ 340 = 200(m - n) \] \[ m - n = \frac{340}{200} = \frac{34}{20} = \frac{17}{10} \] \[ m - n = 1.7 \] Step 4: Test the given values to find a pair (m, n) that satisfies the equation. The list of possible values is \{2.2, 0.8, 0.5, 1.8, 0.3, 0.2\}. We need to find two values from this list, one for m and one for n, such that their difference is 1.7. Let's test the possible values for m:

If \(m = 2.2\), then \(n = m - 1.7 = 2.2 - 1.7 = 0.5\). The value 0.5 is available in the list.
If \(m = 1.8\), then \(n = 1.8 - 1.7 = 0.1\). The value 0.1 is not available in the list.
Other values for m are smaller than 1.7, which would result in a negative value for n, which is not sensible for a price.
Step 5: Final Answer
The only consistent pair of values is \(m = 2.2\) and \(n = 0.5\).