Answer:
a) Equation: 115 - 2.5x = 95 - 2x
ii) x = 40
b) The value of each gift card for which they'll be equal = 15
Step-by-step explanation:
a) Equation for the number of 30 days until the value of the gift cards are equal:
card 1: gift card for 115 that loses 2.50 for each 30-day period
115 - 2.5x - - - - (1)
card 2: gift card for 95 that loses 2 for each 30-day period
95 - 2x - - - - - - (2)
equation for the number of 30 day period (x) for which the amount on card 1 is eqaul to the amount on card 2 is given by:
115 - 2.5x = 95 - 2x
making x the subject of the formula:
115 - 95 = -2x + 2.5x
20 = 0.5x - - - - (i)
x = 20 ÷ 0.5
x = 40
b) the value on the gift card
From expression 1 above; 115 - 2.5x
where x = 40
115 - 2.5x = 115 - 2.5(40)
= 115 - 100 = 15
from expression (2); 95 - 2x
95 - 2(40) = 95 - 80 = 15
∴ The value of each gift card for which they'll be equal = 15
