Asked by Evelyn Domingo on May 18, 2024
Verified
Clara spends her entire budget and consumes 5 units of x and 13 units of y.The price of x is twice the price of y.Her income doubles and the price of y doubles, but the price of x stays the same.If she continues to buy 13 units of y, what is the largest number of units of x that she can afford?
A) 10
B) 5
C) 12
D) 14
E) There is not enough information to say.
Price Of X
Refers to the monetary value or cost assigned specifically to an item or service, denoted here as "X."
Price Of Y
The monetary value or cost assigned to good or service Y, determined by various factors including supply and demand, production costs, and market conditions.
Income Doubles
Refers to a scenario where an individual's or entity's income increases to twice its previous amount.
- Assess how changes in price and income influence a consumer's capability to acquire various goods combinations.
Verified Answer
CC
Cambria ChatmanMay 19, 2024
Final Answer :
A
Explanation :
Initially, let the price of y be PyP_yPy and the price of x be Px=2PyP_x = 2P_yPx=2Py . Clara's initial income is III . Her expenditure on y is 13Py13P_y13Py and on x is 5(2Py)=10Py5(2P_y) = 10P_y5(2Py)=10Py , so her total expenditure (which equals her income) is 13Py+10Py=23Py13P_y + 10P_y = 23P_y13Py+10Py=23Py . Therefore, I=23PyI = 23P_yI=23Py .When her income doubles and the price of y doubles, her new income is 2I=2(23Py)=46Py2I = 2(23P_y) = 46P_y2I=2(23Py)=46Py , and the new price of y is 2Py2P_y2Py . If she buys 13 units of y at the new price, her expenditure on y is 13(2Py)=26Py13(2P_y) = 26P_y13(2Py)=26Py .The remaining income for buying x is 46Py−26Py=20Py46P_y - 26P_y = 20P_y46Py−26Py=20Py . Since the price of x remains 2Py2P_y2Py , the largest number of units of x she can afford is 20Py/(2Py)=1020P_y / (2P_y) = 1020Py/(2Py)=10 .
Learning Objectives
- Assess how changes in price and income influence a consumer's capability to acquire various goods combinations.