The Family Restaurant Order Plan

Build proportional equations for weekly kitchen orders.

From Order Notes to Equations

Model each order using the variables given. Prices have no added taxes or fees.

The family restaurant orders n cartons of mushrooms each week. Each carton costs p dollars. Which equation gives the total cost t in dollars?

A. t = pnB. t = n/pC. t = p + nD. t = p/n

Every case of tomatoes contains 8 cans. Let n be the number of cases ordered and c be the total number of cans.

Complete the equation: c = n

A supplier prices rice by weight. The kitchen pays $21 for 6 pounds. The cost stays proportional to the weight. Let c be the cost in dollars and w be the weight in pounds. Which equation models the order?

A. c = (6/21)wB. c = 3.5wC. c = 21wD. c = 6w

The kitchen orders 3/4 pound of lentils for each batch of soup. Let b be the number of batches planned and w be the pounds of lentils to order.

Complete the equation: w = b

Each bottle of cooking oil holds 2 liters. The kitchen orders only full bottles. Let v be the total liters ordered and n be the number of bottles. Which equation gives n in terms of v?

A. n = 2vB. n = v/2C. n = 2/vD. n = v + 2

Use the Weekly Records

Each table shows a proportional relationship. Use its quantities and units to build an equation.

Let n be the number of bags of onions and c be their total cost in dollars.

Onion Orders
Bags, n	Cost, c ($)
4	26
6	39
10	65

Complete the equation: c = n

Cheese is ordered in sealed packs of equal weight. Let p be the number of packs and w be the total weight in pounds. Which equation gives the number of packs from the weight?

Cheese Orders
Weight, w (lb)	Packs, p
5	4
10	8
15	12

A. p = w/5B. p = (5/4)wC. p = 4wD. p = (4/5)w

The kitchen orders one portion of dry pasta for each planned pasta meal. Let m be the number of meals and w be the pounds of dry pasta ordered.

Pasta Planning
Meals, m	Pasta, w (lb)
16	2
40	5
56	7

Complete the equation: w = m

Nora uses c = 4.8n to model the cost in dollars of n boxes of food-storage bags. What does 4.8 mean in this equation?

A. Each box of bags costs 4.8 dollars.B. Each dollar buys 4.8 boxes of bags.C. The order contains 4.8 boxes of bags.D. Every order costs 4.8 dollars in total.

10.

The kitchen pays $42 for 12 bunches of herbs. Cost is proportional to the number of bunches. Let n be the number of bunches. Complete an equation the family can solve to find how many bunches cost $70.

n = 70

Adjust the Order Plan

Write models for changes to the weekly order. Explain your reasoning on the final question.

11.

A supplier lowers the price of each flour sack from $18 to $15. Let n be the number of sacks and c be their total cost in dollars. Which equation models orders at the new price?

A. c = 15 + nB. c = 18n − 3C. c = 15nD. c = 3n

12.

This week, 2/5 of the planned meals will include roasted vegetables. The kitchen orders 1/2 pound of vegetables for each of those meals. Let m be the total number of planned meals and v be the pounds of vegetables to order.

Complete the equation: v = m

13.

Each crate of peppers contains 6 pounds and costs $27. Let w be the total weight ordered in pounds and c be the total cost in dollars. Write the cost model using weight, not crates.

Complete the equation: c = w

14.

For each planned lunch, the kitchen orders $1.20 worth of chicken and $0.45 worth of rice. Let n be the number of planned lunches and t be the combined ingredient cost in dollars. Amir says two ingredients require two separate equations, so their combined cost cannot be proportional to n. Write one equation for t in terms of n. Explain why the combined cost is proportional.