GKT101: General Knowledge for Teachers – Math

1. A. $7.50+14 P < 60$, $24$ Slices

Strategy

Jacque wants the delivery fee plus the cost of the pizzas to be under $$60$. We can represent this with an inequality whose structure looks something like this:

$\text { (delivery fee })+\text { (cost of pizzas) }[ < \text { or } > ] 60$

Then, we can solve the inequality for $P$ to find how many pizzas Jacque can afford.

1) Which inequality?

• The delivery fee is $$7.50$.
• Each pizza costs $$14$, and $P$ represents the number of pizzas Jacque buys, so the cost of pizzas is $14 \cdot P$.
• Jacque wants the delivery fee plus the cost of the pizzas to be under $$60$, so the total must be less than $$60$.

$\text { (delivery fee })+(\text { cost of pizzas })[ < \text { or } > ] 60$

$7.50+14 P < 60$

2) How many pizzas can Jacque afford?

Let's solve our inequality for $S$

$7.50+14 P < 60$ Subtract $7.50$

$14 P < 52.50$ Divide by $14$

$P < 3.75$

Since she can't buy partial pizzas, Jacque can afford at most $3$ pizzas. And each pizza has $8$ slices, so buying $3$ pizzas gets her $3 \cdot 8=24$ slices.

Let's check our solution

Answers

1) The inequality that describes this scenario is $7.50+14 P < 60$.

2) Jacque can afford at most $24$ slices.

2. D. $24+12 R \geq 100$, $$56$ dollars

Strategy

Sofia needs the sushi she's already ordered plus the additional sushi to be at least $100$ pieces. We can represent this with an inequality whose structure looks something like this:

$\text { (sushi already ordered })+\text { (additional sushi) }[\leq \text { or } \geq] 100$

Then, we can solve the inequality for $R$ to find how many additional rolls Sofia needs to order.

1) Which inequality?

• Sofia has already ordered and paid for $24$ pieces.
• Each roll has $12$ pieces, and $R$ represents the number of additional rolls, so the number of additional pieces from these rolls is $12R$.
• The number of pieces she's already ordered plus the additional pieces needs to be greater than or equal to $100$ pieces.

$\text { (sushi already ordered) }+\text { (additional sushi) }[\leq \text { or } \geq] 100$

$24+12 R \geq 100$

2) How many additional rolls does Sofia need?

Let's solve our inequality for $R$:

$24+12 R \geq 100$ Subtract $24$

$12 R \geq 76$ Divide by $12$

$R \geq 6 .3$

Since she can't order partial rolls, Sofia needs to reserve $7$ additional rolls. And each roll costs $$8$, so ordering $7$ additional rolls costs $7 \cdot \$ 8=\$ 56$.

Let's check our solution

Answers

1) The inequality that describes this scenario is $24+12 R \geq 100$.

2) Sofia needs to spend $$56$ on additional sushi.

3. B. $34+23 F \geq 175$, $7$ bags

The flour Sergei already has plus the flour he buys must be greater than or equal to $175$ kilograms. We can represent this with an inequality whose structure looks something like this:

$\text { (amount he has) }+\text { (amount he buys) }[\leq \text { or } \geq] 175$

Then, we can solve the inequality for $F$ to find how many bags of flour Sergei needs to buy.

1) Which inequality?

• Sergei already has $34$ kilograms of flour.
• Each bag of flour contains $23$ kilograms, and $F$ represents the number of bags he buys, so the amount of flour he buys is $23 \cdot F$.
• The amount of flour he has combined with the amount of flour he buys must be greater than or equal to $175$ kilograms.

$\text { (amount he has) }+(\text { amount he buys) }[\leq \text { or } \geq] 175$

$34+23 F \geq 175$

2) How many bags does Sergei need?

Let's solve our inequality for $F$:

$34+23 F \geq 175$ Subtract $34$

$23 F \geq 141$ Divide by $23$

$F \geq 6.13$

Since he can't buy a partial bag of flour, Sergei needs to buy $7$ bags.

Let's check our solution

Answers

1) The inequality that describes this scenario is $34+23 F \geq 175$

2) Sergei needs to buy $7$ bags to get the amount of flour he needs.

4. $5+2.75 \cdot S \leq 21$, $5$ stops

Strategy

The money Julia spends on her ticket must be less than or equal to the $$21$ she has. We can represent this with an inequality whose structure looks something like this:

$\text { (initial fee) }+\text { (total fees for stops) }[\leq \text { or } \geq] 21$

Then, we can solve the inequality for $S$ to find how many stops Julia can afford.

1) Which inequality?

• The initial fee is $$5$.
• Each stop costs $$2.75$ and $S$ represents the number of stops Julia buys, so she's spending $2.75 \cdot S$ on stops.
• The combined amount of money she spends on her ticket must be less than or equal $$21$.

$\text { (initial fee) }+\text { (total fees for stops) }[\leq \text { or } \geq] 21$

$5+2.75 \cdot S \leq 21$

2) How many stops can Julia afford?

Let's solve our inequality for $S$.

$5+2.75 \cdot S \leq 21$ Subtract $5$.

$2.75 \cdot S \leq 16$ Divide by $2.75$

$S \leq 5 .81$

Since she can't buy partial stops, Julia can afford at most $5$ stops.

Let's check our solution

Answers

1) The inequality that describes this scenario is $5+2.75 \cdot S \leq 21$

2) Julia can afford at most $5$ stops.