Questions: Aisha has 100 saved from her job. She wants to b represents her spending, where x is the number of
4x + 5y < 100
Which ordered pair (x, y) represents a combination
(16,8)
(15,8)
(9,13)
(6,15)
(5,16)
Transcript text: Aisha has $\$ 100$ saved from her job. She wants to b represents her spending, where $x$ is the number of
\[
4 x+5 y<100
\]
Which ordered pair $(x, y)$ represents a combination
$(16,8)$
$(15,8)$
$(9,13)$
$(6,15)$
$(5,16)$
Solution
Solution Steps
To determine which ordered pair (x,y) satisfies the inequality 4x+5y<100, we will substitute each pair into the inequality and check if the inequality holds true. The pair that satisfies the inequality is the correct answer.
Step 1: Define the Inequality
We start with the inequality given in the problem:
4x+5y<100
Step 2: Substitute Ordered Pairs
We will substitute each ordered pair (x,y) from the list into the inequality to check which pair satisfies it.
Step 3: Evaluate Each Pair
For (16,8):
4(16)+5(8)=64+40=104(not valid)
For (15,8):
4(15)+5(8)=60+40=100(not valid)
For (9,13):
4(9)+5(13)=36+65=101(not valid)
For (6,15):
4(6)+5(15)=24+75=99(valid)
For (5,16):
4(5)+5(16)=20+80=100(not valid)
Step 4: Identify Valid Pair
The only ordered pair that satisfies the inequality 4x+5y<100 is (6,15).